An algebra problem by Hobart Pao

Algebra Level 4

If \( C= 1 + \omega^{2} + \omega^{4} + \omega^{6} + \cdots + \omega^{2014} \), where \( \omega \) represents the 2016th root of unity that isn't 1 or \( -1 \), find the value of \( C \).

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