Couple of problems.
1) The definition of "from the Father" changed a few hundred years later to "Father and the Son". And then exploded in 1054.
2) The definition of Trinity has been changed also (can't develop that yet in clear terms).
3) Nicea excommunicated and declared heretical the rule of faith as regards the days/dates of the death, burial, resurrection of our Lord and Saviour Jesus Christ that the church once observed. The church being at earlier times Jesus, Peter, Paul, Mary, and the others.
So, no, Nicea doesn't "work" for at least 1/2 the church (RC) or the saints who came before Nicea.
PS. The idea of infallible ECs is as accurate a concept as infallible Pope
PPS. As to GT using Nicea, I'd guess it's pretty loose since RCers are still allowed to post, but maybe it was changed. Not sure.