# Series diverges or converges

How can I show that $\sum_{n=1}^\infty (\sin n -\sin(πn/2)) / n^2$ converges or diverges? I tried using the ratio test but it's complicated I'd say it converges to $0$ since $n^2$ is growing faster than the numerator.

Hint : $$\left| \frac{\sin n-\sin(\pi n/2)}{n^2}\right|\le \frac{2}{n^2}$$