Help me to solve this trigonometrical equation I want to solve the equation

$$\sin(3x+a)+\sin(3x-a)+\sin(a-x)-\sin(a+x)=2\cos a$$

I solved up to this part
$$\begin{align}
2 \sin 3x \cos a - 2 \cos a\sin x &= 2 \cos a \\
2 \cos a  \left(\;\sin 3x -\sin x \;\right) &= 2 \cos a \\
\sin 3x - \sin x &= 1
\end{align}$$

HINT:
$\sin3x=4\sin x-4\sin^3x$

Alternatively, 
using Prosthaphaeresis Formula,
$$\sin3x-\sin x=2\sin x\cos2x=2\sin x(1-2\sin^2x)=2\sin x-4\sin^3x$$
Then you can use this
