limits - Why does $limlimits_{thetatoinfty}nsinfrac {theta}n=theta$

Questions:

1. Why do we have$$\lim\limits_{\theta\to\infty}n\sin\dfrac {\theta}n=\theta\tag1$$


2. How do we prove $(1)$?

I started off with the well known limit:$$\lim\limits_{\theta\to 0}\dfrac {\sin\theta}{\theta}=1\tag2$$

And substituted $\theta:=\dfrac \theta n$ into $(1)$ to get$$\lim\limits_{\frac \theta n\to 0}\dfrac {\sin\dfrac \theta n}{\dfrac \theta n}=\lim\limits_{\frac \theta n\to0}\dfrac {n\sin\frac \theta n}{\theta}\tag3$$
However after that, I'm not sure what to do. Apparently, the RHS of $(1)$ has a limit of $1$, so that the limit of $n\sin\frac \theta n=\theta$.