How do I solve this $\lim \limits_{n\to\infty} (n/\pi) \cos (2\pi/3n) \sin (4\pi/3n) $? I have to find its value
$$\lim \limits_{n\to\infty} \frac{n}\pi \cos \left( \frac{2\pi}{3n}\right) \sin \left( \frac{4\pi}{3n}\right)$$
Can you please give just clues for solving it?

\begin{equation*}
\begin{split}
\lim_{n\to\infty}\frac{n}{\pi} \cos \frac{2\pi}{3n}\sin \frac{4\pi}{3n}&= \lim_{n\to\infty} \frac{4}{3} \cos \frac{2\pi}{3n}\frac{\sin \frac{4\pi}{3n}}{\frac{4\pi}{3n}}\\
                                                                      &= \frac{4}{3}.(\because \lim_{n\to\infty}\frac{\sin \frac{4\pi}{3n}}{\frac{4\pi}{3n}}=1\ \text{and} \lim_{n\to\infty}\cos \frac{2\pi}{3n}=\cos 0=1)
\end{split}
\end{equation*}
