calculus - Finding limit of a function as it approaches infinity

How do i solve the below without using L'hopital rule. The final answer obtained is $2/3$

$$\lim_{n\to\infty}\frac{\displaystyle{\cot\frac{2}{n}+n\csc\frac{3}{n^2}}}{\displaystyle{\csc\frac{3}{n}+n\cot\frac{2}{n^2}}}$$

How do i go about solving using limit of
$$\lim_{x\to 0}\frac{\sin x}{x}=0,\\
\lim_{x\to 0}\frac{\tan x}{x}=1$$

I was shown to this step but how do i get to it?