The Trinity is the Christian teaching about God. In light of man's experience of God's working in the world, Christians have been driven to assert that God is as he reveals himself. He is Creative Reality (God the Father); he is Expressive Act (God the Son); he is Responsive Power (God the Holy Spirit). Yet he is one God. This is "theology." What matters most, in the Book of Common Prayer, about the Trinity is that we worship God and experience him in a "trinitarian" fashion.
In seminary we used to have great fun, sitting long hours after meals in the refectory making fun of this kind of idiocy. 'I believe in "God the Father"' someone would say making the big scare quotes in the air, 'and in "God the Son" bla bla bla'. Why are the scare quotes? Because you can hear in people's voices the level of their unbelief, the dripping sarcasm that envelopes a word like 'resurrection'.
More on this later, and don't worry, I have more on shoes in the works.