A geometry problem by Abhay Kumar

Geometry Level 4

\[ \cos^2 \left( 1 \cdot \dfrac\pi n \right) + \cos^2 \left( 2 \cdot \dfrac\pi n \right) + \cos^2 \left( 3 \cdot \dfrac\pi n \right) + \cdots + \cos^2 \left( (n-1) \cdot \dfrac\pi n \right) \]

For integer \(n>1 \), find the closed form of the expression above.

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