  It is not known whether the Flint Hills series $\sum_{n=1}^{\infty}
\frac{1}{n^3\cdot\sin(n)^2}$ converges. We show that this question is closely
related to the irrationality measure of $\pi$, denoted $\mu(\pi)$. In
particular, convergence of the Flint Hills series would imply $\mu(\pi) \leq
2.5$ which is much stronger than the best currently known upper bound
$\mu(\pi)\leq 7.6063...$.
  This result easily generalizes to series of the form $\sum_{n=1}^{\infty}
\frac{1}{n^u\cdot |\sin(n)|^v}$ where $u,v>0$. We use the currently known bound
for $\mu(\pi)$ to derive conditions on $u$ and $v$ that guarantee convergence
of such series.
