OKay I tried using a L'Hopital's Rule (immediately failed), series expansion (wrote the first three terms and gave up on this method), Squeeze's Theorem (couldn't get a proper lower bound), and I am absolutely stumped
$\lim_{n\to \infty} \frac{\tan(\pi/n)}{n\sin^2(2/n)}$
According to Mathematica, it converges to $\frac{\pi}{4}$, but I have no idea how. any insight is greatly appreciated