I've been recently interested in the problem of convergence of the function in such form: $\displaystyle \sum_{n=1}^\infty\frac1{n^p\sin^q n}$.

I saw there's been discussion here when [$p=3, q=2$](https://mathoverflow.net/questions/24579/convergence-of-sumn3-sin2n-1) and [$p=2, q=1$](https://math.stackexchange.com/questions/20555/are-there-any-series-whose-convergence-is-unknown) , but wondering if there's any advancement in other cases of variant of the Flint Hills series such as $p=3, q=1$ 

(and also [this post also helped my thought)](https://mathoverflow.net/questions/282259/is-the-series-sum-n-sin-nn-n-convergent)

any relevant paper, article or suggestion will be appreciated. Thanks.