I have arrived at the point where I have a series
$$\sum_{n=1}^{\infty}\frac{\sin^2(n)}{2n}$$
that I know should diverge (checking via python implies it might be divergent, and wolframalpha times out when trying to evaluate it, although yes, it doesn't truly mean anything).
I have tried multiple approaches and convergence tests, but most of them appear to not work with alternating series. Comparing to a harmonic series also didn't lead me anywhere.
Literally out of ideas, does anyone have an approach to this I might be missing?