Checking if some infinite trigonometric sum is convergent

Question

How can I check if this sum (on the natural numbers) is convergent?$$\sum_{n\mod90\neq0}\frac{\tan^2n}{n^3}$$

Answer 1

If the argument is in degrees, this converges since $\tan (x-180)=\tan x$. Thus there is an $M>0$ such that for $n$ not a multiple of $90$ we have $$\tan^2 n\leq M$$ Thus the series converges by comparison to $$\sum \frac M{n^3}$$