The doctrine of the Trinity is a human formulation of a dynamic divine reality. It is inescapable as one ponders the relationships between the Father, and the Son, and the Holy Spirit. A few observations:
1. Muslims tend to be very inflexibly literalistic in their thinking. They "add up" the Father, Son, and HS, and get "three gods". Wrong.
2. The Trinity is not absent in the Old Testament Scriptures; it is implicit. It becomes more explicit in the New Testament. The Bible is a progressive revelation.
3. God is eternally self-sufficient. He has no need of anything or anyone. It is also true of God that he is love -- love is at the core of his being. But, love requires an object to express itself. Combining these two thoughts, we see the logical necessity of the Trinity -- God's self-love. God is love and this love finds eternal expression within his eternally self-sufficient being.
The Father loves the Son (we see this expressed in the gospels); the Son loves the Father (we certainly also see this expressed in the gospels) and the Spirit of God expresses the unity between the two of them.
4. You see the triangle in the diagram. Think of a musical triangle consisting of three continuous sides.
- regardless of which side you strike, the exact same note is sounded -- they speak and act as one
- you hit one side, all three sides resonate and contribute to the sound that is made -- they speak and act as one -- it is impossible for one to act apart from the others. (The exception being the crucifixion in which a terrible rent in the godhead was made as the Father "excommunicated" the Son who had become sin for us -- and the eternal Son experienced the hell of separation from God.)
A lot of the early Church schisms were due to trying to parse God's trinity and Christ's humanity/divinity to the nth degree. Christians should retain a sense of mystery. Mystery is at the heart of reality. Not everything is knowable. Not everything is reducible to materialistic explanations. Not everything is reducible to logical constructs. Some things are incomprehensible, other things are inexpressible.
A God who is completely comprehensible by us is probably a God who has been falsely defined and understood.
Which would be a pretty good definition of Islam.