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.