CB's initial question to you asked where the Council of Nicea GOT the idea of defining the Trinity. They did NOT just invent the doctrine. They knew what the Apostles taught, what Jesus taught and what the Bible said concerning the nature of Almighty God and how He has revealed Himself to mankind. They took this knowledge and came up with a succinct and easy to learn "creed" that put into words what Scripture clearly taught. It was certainly in answer to heretical sects that flared up from the start that questioned the Deity of Jesus Christ and it addressed and defined what the Trinity is so that Christians would not be confused and tripped up by these heretics. From http://en.wikipedia.org/wiki/Trinity:
The corresponding word in Greek is Τριάς, meaning "a set of three" or "the number three".[8]
The first recorded use of this Greek word in Christian theology (although not about the Divine Trinity) was by Theophilus of Antioch in about 170. He wrote:[9][10]
In like manner also the three days which were before the luminaries, are types of the Trinity [Τριάδος], of God, and His Word, and His wisdom. And the fourth is the type of man, who needs light, that so there may be God, the Word, wisdom, man.[11]
Tertullian, a Latin theologian who wrote in the early 3rd century, is credited as being the first to use the Latin words "Trinity",[12] "person" and "substance"[13] to explain that the Father, Son, and Holy Spirit are "one in essencenot one in Person".[14]
So, the Council of Nicea did not invent the doctrine of the Trinity. They defined it as Scripture did. One can believe in the Trinity without having to accept everything that Nicea put forth because it is a Biblical doctrine found in Scripture.
“what the Bible said concerning the nature of Almighty God”
What edition did they cite?