Help with finding the $\lim_{x\to 0} \tan x \csc (2x)$ So I am trying to figure out the limit

$$\lim_{x\to 0} \tan x  \csc (2x)$$

I am not sure what action needs to be done to solve this and would appreciate any help to solving this.
Hint: We have $\csc(2x)=\frac{1}{\sin(2x)}$ and $\sin(2x)=2\sin x\cos x$.
$$
\lim_{x\to 0} \tan x  \csc (2x)= \lim_{x\to 0} \dfrac{\sin x}{2\cos^2x\sin x} = 1/2
$$