The word Trinity has never appeared in the bible but the concept of one God in three persons are biblical perspectives. Jesus reveals to us about the three persons of God: God the Father and God the Son and God the Holy Spirit. The three person of God exist in one divinity and that all three are one God, one substance, but three Persons or individuality. The saying Jesus told his apostles was to confirm the three persons of God that He will send the Spirit from the Father and the Spirit shall testify His teaching (Jn 15, 26). Before his exaltation Jesus commands his disciples to baptize people in His name and that they become children of God through baptism with the universal formula: I baptize you in the name of the Father and of the Son and of the Holy Spirit (Mat 28,19).
From infinite to finite, without Jesus' revelation we know nothing about the doctrine of the Trinity. We don't even know how to form a question to start with. Jesus reveals to us about God the Father and God the Son and God the Holy Spirit, each independent from other, equal in majesty and yet united in one God. Many theologians try hard to learn more about the mystery of the Trinity but they all failed because the mystery is incomprehensible. It is beyond human logic because, put in the language of the prophet Isaiah: God's thoughts are not ours and heavens are higher than earth, so God's ways are higher than ours. (Is 55,8) How could a human mind understand the divine's mind and how could the corruptible understand the incorruptible. How could the creatures undermine the Deity unless it is revealed to?
When we approach to the mystery with deep love for God we will understand the mystery a bit more; only love can understand love, even a finite love can understand a bit of infinite love. We love God in order to understand God's love for us and it is not the other way round. If we want first to understand what God's love is before we commit ourselves to love God then we can go not very far. If we could understand the mystery of the Trinity then it is a mystery no more and the revelation in the Bible would be divine no more but it is only human intelligence designed. The mystery of God's love for us teaches us that the more we try to understand the mystery the more we divorce from it because we are limited both in wisdom and intelligence. With a humble heart this recognition helps us to see that apart from Jesus our human wisdom is incapable of knowing the mystery of the Trinity. The mystery of God's love is hidden from our eyes when we approach God with our own wisdom and knowledge but when we surrender our wisdom and see with the eyes of faith we will have some knowledge of the mystery of God's love. Faith substitutes for our lack of limitations. With faith in Jesus we will overcome our inability to see. The doctrine of the trinity is part of God's revelation of God who is infinite to us who are finite.
The doctrine of the Trinity is the special gift of Christianity, setting it apart from the rest of the world's religions. Some of them have a set triad of divinities, such as the Hindu triad of Brahma, Vishnu and Schiva but their teaching has nothing in common with the Trinity except the notion of triad.