2001 AIME II Problem 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\leq\theta_{1} < \theta_{2} < \ldots < \theta_{2n} < 360 and angles are measured in degrees. Find the value of \theta_{2} + \theta_{4} + \ldots + \theta_{2n}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.