How do we prove, without actually expanding, that

$$\begin{vmatrix} 
\sin {2A}& \sin {C}& \sin {B}\\
\sin{C}& \sin{2B}& \sin {A}\\
\sin{B}& \sin{A}& \sin{2C}
\end{vmatrix}=0$$

where $A,B,C$ are angles of a triangle?

I tried adding and subtracting from the rows and columns and I even tried using the sine rule, but to no avail.