Question 14
There are $2n$ 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 $0 \le \theta_{1} \lt \theta_{2} \lt \ldots \lt \theta_{2n} \lt 360$ and angles are measured in degrees. Find the value of $\theta_{2} + \theta_{4} + \cdots + \theta_{2n}.$