sequences and series - Convergence of $sum_{n=1}^infty frac{sin^2(n)}{n}$

Does the series

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

I've tried to apply some tests, and I don't know how to bound the general term, so I must have missed something. Thanks in advance.

Answer

Hint:

Each interval of the form $\bigl[k\pi+{\pi\over6}, (k+1)\pi-{\pi\over6}\bigr)$ contains an integer $n_k$. We then have, for each $k$, that ${\sin^2(n_k)\over n_k}\ge {(1/2)^2\over (k+1)\pi}$. Now use a comparison test to show your series diverges.