Evaluate: ∫₀^(2π) (xcot x)/(cosec x + cot x) dx, x ≠ π

The integrand as printed, $\dfrac{x\cot x}{\operatorname{cosec} x + \cot x} = \dfrac{x\cos x}{1 + \cos x}$, is not integrable over $[0, 2\pi]$ because of the singularity at $x = \pi$ (the integral diverges), so the printed integrand has probably been misread. Answer held until the owner checks the paper.