> Determine the autocorrelation $r_{xx}[m]$ of the discrete signal 

$$x[n] = (\sin{2\pi fn)}.$$

where $n$ and $m$ are integers. 

Using the definition I get

$$\begin{align}
r_{xx}[m] &= \sum_{n=-\infty}^{\infty}x[n]x[n-m] \\
&= \sum_{n=-\infty}^{\infty}\sin{(2\pi fn)\sin{(2\pi f(n-m))}} \\
&= \sum_{n=-\infty}^{\infty}\sin{(2\pi fn)\sin{(2\pi fn - 2\pi fm))}} \\
\end{align}$$

but I can't seem to figure it out from here. I've tried using different trigonometric identities without result. I'm guessing it's something simple I'm missing.