Evalute $\lim\limits_{n\to\infty}\sin^2(\pi\sqrt{ n^2+n})$. I like to  find the following limit:

$\lim\limits_{n\to\infty}\sin^2(\pi\sqrt{ n^2+n})$.

Any ideas or insight would be greatly appreciated.

Hint: Note that 
$$\sqrt{n^2+n}=\sqrt{n^2+n}-n+n=\frac{n}{\sqrt{n^2+n}+n}+n=\frac{1}{\sqrt{1+1/n}+1}+n.$$
