a, x, y, z are real numbers such that:

$\displaystyle \frac{cosx + cosy + cosz}{cos(x+y+z)}= \frac{sinx + siny + sinz}{sin (x+y+z)} = a$

Using the identity, a = $\displaystyle \frac{cosx + i sinx + cosy + i siny + cosz + i sinz}{cos(x+y+z) + isin(x+y+z)}$

show that:

$\displaystyle a = cos(y+z) + cos(x+z) + cos(x+y)$

thanks