Prove that `sum_(k=1)^(n-1)(n-k)cos(2kpi)/n=-n/2`, where`ngeq3` is an integer

Explanation

To prove that

\[ \sum_{k=1}^{n-1} (n-k) \cos\left(\frac{2k\pi}{n}\right) = -\frac{n}{2} \]

where \( n \geq 3 \) is an integer, we will follow these steps:

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