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Evaluate the definite integral:

$$\int_{0}^{\pi /2} \cot \bigg(\frac{x}{2} \bigg) (1-\cos ^4x).dx$$

Could something give me hint as how to proceed in this question? I tried factorising $(1-\cos ^4x)$ and using $1-\cos ^2x=\sin^ 2x$ but the expression does not simplify.

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HINT: show that your integrand is given by $$\sin \left( x \right) \left( 1+\cos \left( x \right) \right) \left( \left( \cos \left( x \right) \right) ^{2}+1 \right) $$

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