Convergence of $\sum_n \frac{|\sin(n^2)|}{n}$

A problem in Makarov's Selected problems in real analysis asks to investigate the convergence of $\displaystyle \sum_n \frac{|\sin(n^2)|}{n}$

I'm clueless at the moment. I can't find any good property of the sequence $|\sin(n^2)|$.

$|\sin(n^2)|$ is small whenever $n\sim \sqrt{p\pi}$, and, as $p\to \infty$, the $\sqrt{p\pi}$ get closer to each other since $\sqrt{(p+1)\pi}-\sqrt{p\pi}\sim \frac 12 \sqrt{\frac{\pi}{p}}$.

Any hint is appreciated.