There is a right triangle \triangle A B C, in which \angle A is the right angle. On side A B, there are three points X, Y, and Z that satisfy \angle A C X=\angle X C Y=\angle Y C Z=\angle Z C B and B Z=2 A X. The smallest angle of \triangle A B C is \frac{a}{b} degrees, where a, b are positive integers such that G C D(a, b)=1. Find a+b.