Prove that \( \int _{ 0 }^{ \pi }{ \frac { { sin }^{ 2 }n\theta }{ { sin }^{ 2 }\theta } } d\theta =n\pi, where \quad n \quad is \quad a \quad natural \quad number. \) I tried differentiating under the integral but I got stuck. I also tried mathematical induction but I got stuck there too. Please help.

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