# 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.

×