Find $\lim_{n\to\infty} \sqrt{n}a_n$

Question

Define $a_n$ is real sequence which satisfies

$$a_1=1, \quad a_{n+1}=\sin(a_n)$$

Find $$\lim_{n\to\infty} \sqrt{n}a_n$$

I just know $$\lim_{n\to\infty} a_n = 0$$

but I don't know what should I do.

I'm interested in two solutions (using Stolz-cesaro, without using stolz-cesaro).