Convergence of the Flint Hills series

Corollary 1.2: $\sum_{n\ge1}1/(n^3\sin^2 n)$ converges, deduced from $\mu(\pi)=2$ via a dyadic spacing estimate valid for any exponent below $5/2$. More generally $\sum n^{-a}|\sin n|^{-b}$ converges iff $a>\max\{1,b\}$ (Corollary 5.2). No value or numerical estimate of the sum is given.

Corollary 1.2: $\sum_{n\ge1}1/(n^3\sin^2 n)$ converges, deduced from $\mu(\pi)=2$ via a dyadic spacing estimate valid for any exponent below $5/2$. More generally $\sum n^{-a}|\sin n|^{-b}$ converges iff $a>\max\{1,b\}$ (Corollary 5.2). No value or numerical estimate of the sum is given.