calculus - Finding limit of $frac{nsin n!}{n^2+1}$ as $n$ approaches infinity

I tried to find $$\lim_{n\to \infty}\dfrac{n\sin n!}{n^2+1}$$ using the squeeze (or sandwich) theorem, and I got the result $0$. Is this right? Because the limit as $n$ approaches infinity of $\sin(n)$ is not defined.