Convergence of $\sum_{n\geq1}\frac{\sin^n(n)}{n}$

Determine whether the sum converges $\sum\limits_{n=1}^{\infty} \frac{\sin^n(n)}{n} $

I tried to use all the standard signs, but there's nothing to understand about them in general. It seems to me that the problem is connected with the approximation of the number pi by rational numbers, but I could not bring this idea to the end.