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.

Hint. We have that
$$\sin(720/600\cdot n\cdot\pi)=\sin((2-4/5)\cdot\pi\cdot n). $$
Then recall that $\sin(x+2n\pi)=\sin(x)$ and $\sin(-x)=-\sin(x)$ for all $x\in\mathbb{R}$ and $n\in\mathbb{Z}$.
