Evaluating $\lim\limits_{n \to \infty }\sqrt[n]{ \frac{\left | \sin1 \right |}{1}\cdot\cdot\cdot\frac{\left | \sin n \right |}{n}} $ Help me please with the limit:

$$\lim_{n \to \infty }\sqrt[n]{ \frac{\left | \sin1 \right |}{1}\cdot\frac{\left | \sin2 \right |}{2}\cdot\cdot\cdot\frac{\left | \sin n \right |}{n}}$$

Thanks!
$$\sqrt[n]{ \frac{\left | \sin1 \right |}{1}\cdot\frac{\left | \sin2 \right |}{2}\cdot\cdot\cdot\frac{\left | \sin n \right |}{n}}  \leq \sqrt[n]{\dfrac1{n!}}$$ Now our good old Stirling's formula will do the job.
With AM-GM the sequence is smaller than $\frac{H_n}{n}$ with Hn is équivalent ln (n) , then the limite is zéro.