This threefoldness is present throughout the whole New Testament not as a formal statement but as a pattern to be seen everywhere. Some of the early church father used a remarkable expression. The doctrine of the Trinity is the end of all pantheism. He does not need this world in order to come to his full potential. In the revelation of the Father through the Son by the Spirit we not only receive some external information about God but we have the guarantee that God himself is speaking to us and opening his divine heart to us.
Revelation is really and fully self-explanation.
But above all the doctrine of the Trinity is of important for our salvation. It is the answer to our question whether or not our salvation is really God's work. In the final analysis this is the reason why the church is so vitally interested in the divinity of Jesus Christ and the divinity of the Holy Spirit. None of this is bald theory. It is echoed in the Christian personal experience.