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I want to prove this equation:

[tex] \cos\left(\frac{2\pi}{5}\right)+\cos\left( \frac{4\pi}{5}\right)+\cos\left( \frac{6\pi}{5}\right)+\cos\left(\frac{8\pi}{5} \right) = -1 [/tex].

I've no idea how to begin. I think it may be related to complex numerd but I don't know how to combine them.

[tex] \cos\left(\frac{2\pi}{5}\right)+\cos\left( \frac{4\pi}{5}\right)+\cos\left( \frac{6\pi}{5}\right)+\cos\left(\frac{8\pi}{5} \right) = -1 [/tex].

I've no idea how to begin. I think it may be related to complex numerd but I don't know how to combine them.

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