calculus - I need help computing the following limit using only squeeze theorem and basic limit properties

I was able to compute the limit of the following using l'Hopital's rule, and found it to be $\frac{\pi}{4}$, but apparently there is a way to evaluate the limit using the squeeze theorem, apparently you have the fact that the area of a sector of a circle with radius 1 squeezes between the area of a larger triangle and smaller one for small angles

Here is the limit:

$\displaystyle \lim_{n \rightarrow \infty} \dfrac{\tan\left(\dfrac{\pi}{n}\right)}{n\sin^2\left(\dfrac{2}{n}\right)}$