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hmm to make the math work maybe you should split it into 2 integrals with limits (0,pi) and (pi,2pi)

Here is my (wrong) calculation so far:

The second integral goes from pi/2 to what?

correction: it's \[\int\limits_{0}^{\pi} \] and \[\int\limits_{\pi}^{2\pi}\]

So I did the integral wrong?

Thank you so far for your help sirm3d.

\[\cos^2 A=\frac{ 1 }{ 2 }(1+\cos 2A)\] that's half-angle identity

im still checking your solution.

\[\sqrt{4-4\cos^2t}=2\sin t\] in \[0

Thank you for your help, sirm3d. I try to be more carefull next time. :)
Thx a lot.