15. Here are two properties enjoyed by automorphisms of the upper half-plane. (a) Suppose is an automorphism of H that fixes three distinct points on the real axis. Then is the identity. (b) Suppose (x, x2, x3) and (y, y2, y3) are two pairs of three distinct points on the real axis with and y1 < y2 < y3. Prove that there exists (a unique) automorphism of H so that (x;) = Yj, j1, 2, 3. The same conclusion holds if y3 < y < y2 or y2 < Y3 < y1. x1 < x2 < x3