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 \(\theta_{2} + \theta_{4} + \ldots + \theta_{2n}\).

(第十九届AIME2 2001 第14题)