The trinity is a very old doctrine. See The Trinitarian Old Testament for just how old.
But the council of Nicea gave us certain terminology that is accepted by both East and West. The creed that came from it (and here I refer to the Niceno-Constantinopolitan creed of 381) is basic to all Christian churches. Yet its doctrine of God is a particular one - one that is sometimes unwittingly (sometimes wittingly) side-lined, ignored or opposed.
The first thing to notice is Nicea's doctrine of 'the one God.' To the untrained eye, it looks like it doesn't have one. It simply says 'We believe in one God' and then immediately goes on to speak of 'the Father Almighty', 'one Lord Jesus Christ' and 'the Holy Spirit'. In this it follows Paul in 1 Corinthians 8:6
"For us there is but one God, the Father, from whom all things came and for whom we live; and there is but one Lord, Jesus Christ, through whom all things came and through whom we live."
The one God and the one Lord are the Father and the Son. It is not the case that the one God is the omni-being of philosophical theism and the Persons are sub-species of this divine stuff. No. Nicea gives absolutely no definition of the one God except to unfold His being in the description of the Three.
No doubt many later theologians would have loved to have travelled back in time to Nicea and inserted a lengthy treatise on the 'omnis' somewhere between "I believe in God..." and "...the Father Almighty". But Nicea doesn't go there. There's not even a footnote between the two. The one God is the Father Almighty, to Whom is joined the Lord Jesus Christ in the unity of the Spirit who is the Lord, the Giver of life. Athanasius and co. will not let you force a breach between a description of the One and the Three. To describe the One is to unfold the Three.
And what does Nicea tell us about the ousia (being) of this triune God? Again a typical western theologian may be disappointed. The only reference in the creed to this 'ousia' is that controversial phrase 'homo-ousios'. Jesus, the Son, is 'homo-ousion tw patri' (of one being with the Father). Please note, the creed does not give us a prior definition of 'ousia' which is then mapped onto the three Persons. (See these diagrams). Instead we infer what the 'ousia' is from the fact that Father and Son are 'homo-ousios'.
Jesus, in all His difference from the Father - i.e. born of a virgin, crucified, buried, raised, ascended - is still homo-ousios with the Father. In His difference He is divine. And in His divinity He is 'God from God, Light from Light, True God from True God, begotten not made." Even in His divinity He is 'ek tes ousia tw patri' (out of the being of the Father). There are important differences between Father and Son that are not papered over but rather affirmed by, and included in, the homo-ousios.
The homo-ousios does not denote three-fold repetition but rather, in TF Torrance's words:
"The Father/Son relationship falls within the one being of God.” (Trinitarian Faith, p119).
Homoousios “meant that the Son and the Father are equally God within the one being of God.” (ibid, p122)
The homo-ousios upholds the distinction (as well as unity) of Father and Son. Remember that you can't be 'homo' with yourself. And it points us to the fact that the Father is Begettor, the Son Begotten. The Father from Himself, the Son from the Father (even according as He is God, contra Calvin but with Nicea!).
There are genuine differences in Persons that in no way compromise their equality of divinity. There is never a time when the Son is not homo-ousios with the Father nor is there a time when the Son is not begotten of His Father. Therefore there is not an ousia of the Father that could ever be separately conceived and then assigned in equal measure to Father, Son and Spirit. Instead the ousia of God is a mutually constituting communion in which Father, Son and Spirit share. The ousia of the trinity consists in three Persons who are 'homo' with one another. While Nicea does not say explicitly that the 'ousia' is the communion of Persons, it points decidedly in this direction. (See Torrance's 'Trinitarian Faith' for more).
All this is to say that distinctions between Father, Son and Spirit are upheld within the divine nature. The divine nature is not a set of pre-determined attributes which are identically mapped onto the Three. The divine nature is constituted by difference, distinction, mutuality, reciprocity - it is a divine life (a dance even!) not a divine stuff.
Compare this with so much doctrine of God in the west. First an ousia of 'omnis' is determined. The one God is discussed for 600 pages in terms of 'uncreated Creator'. And then we face the Three. What do we then do? Simply give to each Person this CV of attributes and insist that this is what the Nicene homo-ousios demanded! On this understanding all difference, distinction, mutuality and reciprocity is banished from the status of deity. In preference to the lively interplay of Father, Son and Spirit, a 'simple' doctrine of the One is forwarded. And God's own being is conceived of as a stuff not a life.
Think I prefer Nicea!