The questions arising out of man's finitude are answered by the doctrine of God and the symbols used in it. The questions arising out of man's estrangement are answered by the doctrine of Christ and the symbols applied to it. The questions arising out of the ambiguities of life are answered by the doctrine of the Spirit and its symbols.This is a nice summary, not only of Tillich's thoughts on the Trinity, but of his system as a whole. It is good to keep in mind that Tillich feels that he is doing apology, that is, he is trying to make the Christian doctrine meaningful to modern humans. It is not metaphysical speculation. Therefore there is no conflict between this and "my" trinity, but you can probably see where I got the idea from.
Systematic theology III, 286
(My three existential problems are also based loosely on Tillich, on some ideas found in his The Courage to Be.