AMC 12 2006a Problem 15

Suppose $\cos x=0$ and $\cos (x+z)=1/2$. What is the smallest possible positive value of $z$?

$\mathrm{(A) \ } \frac{\pi}{6} \mathrm{(B) \ } \frac{\pi}{3} \mathrm{(C) \ } \frac{\pi}{2} \mathrm{(D) \ } \frac{5\pi}{6} \mathrm{(E) \ } \frac{7\pi}{6}$