Another curious identity

Geometry Level 3

cos(12)+cos(84)+cos(132)+cos(156)= ?\large \cos(12^\circ)+\cos(84^\circ)+\cos(132^\circ)+\cos(156^\circ)= \ ?

Extra Credit Problem: Can you generalize this result by writing an analogous equation involving cos(360n)\cos\left(\frac{360^\circ}{n}\right) for any positive integer nn?

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