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 <a href="http://en.wikipedia.org/wiki/Dirichlet%27s_approximation_theorem">Dirichlet's approximation theorem</a>,
but the problem is to prove that it is $0$.