limits - Evaluate: $ lim_{xto +infty} {x^3cos(1/x)over sin x} $

I'm trying to evaluate the following limit but I'm stuck.

$$
\lim_{x\to +\infty} {x^3\cos(1/x)\over \sin x}
$$

I tried the squeeze theorem but I was led to a dead-end. Any help would be appreciated.