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I am trying to see if the following integral converges, and if it has a simple solution

$\int_{0}^{2\pi}\int_{0}^{2\pi}\frac{\cos(\theta_1-\theta_2)}{\sqrt{1-\cos(\theta_1-\theta_2)}}d\theta_1d\theta_2$.

So far, the integral is eluding me. At first I thought about writing it as a Fourier series, but this does not help me solve the integral.

Any help or guidance would be appreciated.

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    $\begingroup$ The integral divereges. $\endgroup$
    – Mark Viola
    Mar 26 '21 at 14:24
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Mathematica says the integral converges to $(2\sqrt{2}\pi^2)i$. So it probably involves a complex substitution. I'm working on it. I will let you know if I figure it out.

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