Evaluate: `int_0^pi(xsin2xsin(pi/2cosx)/(2x-pi)dx`

Explanation

To evaluate the integral

\[ I = \int_0^{\pi} \frac{x \sin(2x) \sin\left(\frac{\pi}{2} \cos x\right)}{2x - \pi} \, dx, \]

we will use a property of definite integrals. The property states that:

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