How to prove $\frac{\cos\theta * \theta}{\sin\theta}$ = $\frac{\sin\theta}{\theta}$

How to prove $\frac{\cos\theta * \theta}{\sin\theta}$ =
$\frac{\sin\theta}{\theta}$

I am working on a problem that is looking to prove
$\lim_{x\to0}\frac{\sin\theta}{\theta}$ = 1. At the particular point I am
working on, I have to prove 1 $<$ $\frac{\theta}{\sin\theta}$ $<$
$\frac{1}{\cos\theta}$ can be written as $\cos\theta$ $<$
$\frac{\sin\theta}{\theta}$ $<$ 1. I assume that you need to multiply
everything by $\cos\theta$, but I am not sure how to prove that
$\frac{\cos\theta * \theta}{\sin\theta}$ = $\frac{\sin\theta}{\theta}$.