How to Solve the Integral of Sin(2Cos(θ))Cos(2nθ) from 0 to π?

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\int^{\pi}_{0}Sin(2Cos(\theta))Cos(2n\theta)d\theta

I can apply some software to do this integral. However, I need some procedures for this integral. Any help is welcome
 
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can you to n=0, n=1, n=2 ? Is there a pattern?
 
g_edgar said:
can you to n=0, n=1, n=2 ? Is there a pattern?

Yes. n is any integer
 

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