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How to calculate the infinite series $\sum_{n=1}^{\infty }\sin(nx\pi)\sin(ny\pi)$ where $x,y$ are real numbers?

I assume this is related to Fourier series, but I can't calculate this.

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    Is there a reason you expect this to converge, in general? If $x=y$ is irrational, for example, then $\sin^2(nx\pi)$ does not converge to $0$.2012-11-14

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