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Question Number 135034 by mnjuly1970 last updated on 09/Mar/21

$$...nicecalculus$$$$ifn⩾2and{P}_n=\underset{n=1}{\prod ^{n-1}}sin\left(\frac{k\pi }{n}\right)$$$$find::{lim}_{n\to \mathrm{\infty }}\frac{{nP}_n}{2}{\int }_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{cos\left(3x\right)}{{sin}^n\left(x\right)}dx$$

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