real analysis - Does $sum _{n=1}^{infty }frac{left|sinleft(nright)right|}{n}$ converge?

I'm not sure whether the following series converges or diverges:
$$\sum _{n=1}^{\infty }\frac{\left|\sin (n)\right|}{n}$$

I proved that the series $\sum _{n=1}^{\infty }\frac{\sin^2 (n )}{n}$ converge. Is there a way I can use that? I've tried using Dirichlet series test with the latter but didn't got nowhere since $\frac{1}{\left|\sin x\right|}$ is not monotone decreasing.

Answer

$$ \frac{\sin^2(n)}{n} = \frac{1}{2n} - \frac{\cos(2n)}{2n} $$
By Dirichlet's test, $\sum \frac{\cos(2n)}{2n} $ converges, hence $\sum \frac{\sin^2(n)}{n} $ diverges (since $\sum \frac{1}{n}$ diverges to $\infty$).
$$ \frac{\sin^2(n)}{n} \leq \frac{|\sin(n)|}{n}$$
So by the comparision test, $\sum \frac{|\sin(n)|}{n} $ diverges