How does it derived from LHS term $$\sin\left(\frac{720n\pi}{600}\right) = -\sin\left(\frac{4n\pi}{5}\right).$$
It is a part of derivation I found in an example but this step is not clear to me if I tried to just divide and use reminder but it is not same and $\sin(n\pi) = 0$ so it is not near to above step. 
Please explain.

$$\sin{(720/600 n \pi)}$$$$=\sin{(6/5 n \pi)}$$$$=\sin{((2-4/5) n \pi)}$$
$$=\sin{(2 n \pi-4/5n\pi)}$$$$=\sin{(-4/5 n \pi)}$$$$=-\sin{(4/5 n \pi)}$$
