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(Solved): step by step please  Problem 10.5. Bonus: Compute \[ \sum_{n=1}^{\infty} \frac{\sin ^{2}(n \alp ...



step by step please 

Problem 10.5. Bonus:
Compute
\[
\sum_{n=1}^{\infty} \frac{\sin ^{2}(n \alpha)}{n^{2}} .
\]
Hint: Consider the Fouries series
Problem 10.5. Bonus: Compute \[ \sum_{n=1}^{\infty} \frac{\sin ^{2}(n \alpha)}{n^{2}} . \] Hint: Consider the Fouries series of the function which is equal to 1 for \( |x|<\alpha \), and 0 for other \( x \in(-\pi ; \pi) \).


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To compute this sum, we will use the hint provided and consider the Fourier series of the function that is equal to 1 for |x| < ?, and 0 for
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