ISL 1989 Problem 70

Given that $$\frac{\cos(x) + \cos(y) + \cos(z)}{\cos(x+y+z)} = \frac{\sin(x)+ \sin(y) + \sin(z)}{\sin(x + y + z)} = a,$$ show that $$\cos(y+z) + \cos(z+x) + \cos(x+y) = a.$$