2001 AIME II Problem 14

There are 2 n complex numbers that satisfy both z^{28}-z^{8}-1=0 and |z|=1. These numbers have the form z_{m}=\cos \theta_{m}+i \sin \theta_{m}. where 0 \leq \theta_{1}<\theta_{2}<\ldots<\theta_{2 n}<360 and angles are measured in degrees. Find the value of \theta_{2}+\theta_{4}+\cdots+\theta_{2 n}.