Integral of $$$\frac{\sin{\left(2 x \right)} \cos^{4}{\left(x \right)}}{\sin^{4}{\left(x \right)}}$$$
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Find $$$\int \frac{\sin{\left(2 x \right)} \cos^{4}{\left(x \right)}}{\sin^{4}{\left(x \right)}}\, dx$$$.
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