Liouville-Roth Irrationality Measure of $\pi$ = 2 already proven?

Question

I was looking through this paper and I was curious. Has it already been established that the Flint Hills series $\displaystyle\sum_{n\in\mathbb{Z}^{+}}\frac{\csc^2 n}{n^3}$ converges? And has it already been established that the Liouville-Roth irrationality measure of $\pi$ is equal to 2?