# Finding Values

Geometry Level 5

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 $$\theta_{2} + \theta_{4} + \ldots + \theta_{2n}$$.

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