I_{n}=\int_{0}^{\pi }\frac{1-\cos nx}{1-\cos x}
\\
I_{n}=\int_{0}^{\pi }\frac{1-(1-2\sin ^{2}\frac{nx}2{})}{1-(1-2\sin ^{2}\frac{x}{2})}
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=\int_{0}^{\pi }\frac{\sin ^{2}\frac{nx}{2}}{\sin ^{2}\frac{x}{2}}
\\
Let\ \theta =\frac{x}{2}
result follows not good at writing it