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.

$$\frac{720}{600} = \frac{72}{60}=\frac{12}{10}=\frac{6}{5} = 2 - \frac{4}{5}.$$
Now you write $$\sin\left(\frac{\pi n \cdot 720}{600}\right) =\sin\left( 2\pi n -\frac{\pi n \cdot 4}{5}\right) =  \sin\left(-\frac{\pi n \cdot 4}{5}\right) =-\sin\left(\frac{\pi n \cdot 4}{5}\right)$$
