[kinkrtyavimoodh]

I think it's not obvious but it reduces to a relatively 'common' integral.

1 - cos(x) can be written as 2*cos^2(x/2)

Take the logarithm and you get 2ln (cos(x/2)), which is relatively common and the solution is https://www.quora.com/How-do-I-integrate-log-cos-x-from-0-to...