Return to Question

I can prove that the inferior limit exists by using the Dirichlet's approximation theorem, but I cannot prove it is $0$.

Is it true that $\varliminf_{n \rightarrow +\infty} |n \sin n| = 0$, where $n$ runs over the integers?

The existence of the limes inferior follows from Dirichlet's approximation theorem, but the problem is to prove that it is $0$.