It'a actually a common misconception that the council of Nicea developed or established the concept or theology of the Trinity on July 19, 325 AD. The focus of the council of bishops was the discussion on the cult theology of Arianism as proposed by the silver-tongued presbyter Arius. Given the previous centuries of Christian persecution prior to this brief era of peace Constantine convened the bishops to discuss this uprising lead by Arius in order to prevent further strife and dissension within the church and preserve the era of peace.
Arius believed that Christ was not the eternal Son of God, but was actually created by God the Father. Arius pushed for others to accept this theology. The concept of the Trinity (Father, Son and Holy Spirit) was not developed or established at this point, it was defended as it was already fully represented in scripture and demonstrated during Christ's ministry.
During Jesus' ministry the jewish Sanhedrin approached the Roman government for assistance in capturing, punishing and killing Jesus Christ because of his "blasephemous claims of divinity"...that Christ claimed that he was in fact the Son of God and fulfillment of prophetic scripture from centuries past. The quality of Christ's divinity was called into question by Arius, but the council rejected the cult of Arianism and thereby publically came together and unified the theology they had taught for centures (and was passed to them from Christ and his apostles) via the Nicene Creed. The only thing they may have developed (or coined) was the term "Trinity".
There is an alternative version of the story of Christ's death.
The Sanhedrin did not ask the Romans to kill Jesus. The Jews had a long history of rebellion against Rome, and Christ was being called The King of the Jews because so many people believed Him to be the Messiah.
Hearing this, the Romans (specifically, Pontius Pilate, the Procurator of the region) arrested Jesus. He was ordered executed by the Romans when He refused to acknowledge the Emperor as the ultimate authority over the Jewish people. It is true that the Jewish authorities were hostile toward Him, but the Jews hated the Romans and did not ask them to kill anyone.
Many people believe Christ never claimed divinity in His lifetime.