Series

I have the suspicion that the following series converges, but how would I prove it? I'm guessing that for some n, $\sin(\frac{1}{n^2}) < \frac{1}{n^2}$ so, as the later converges, the former must, too. But how should I prove it?

$\sum_{n=1}^\infty |\sin(\frac{1}{n^2})|$