how can i prove this trigonometry equation I need help on proving the following:
$$\frac{\cos {7x} - \cos {x} + \sin {3x}}{ \sin {7x} + \sin {x} - \cos {3x} }= -\tan {3x}$$
So far I've only gotten to this step:
$$\frac{-2 \sin {4x} \sin {3x} + \sin {x}}{ 2 \sin {4x} \cos {3x} - \cos {x}}$$
Any help would be appreciated as trigonometry is not my forte.

The LHS can seen as $$\frac{\cos 7x -\cos x + \sin 3x}{\sin 7x + \sin x - \cos 3x} = \frac{-2\sin 4x \sin 3x + \sin 3x}{2\sin 4x\cos 3x - \cos 3x} = \tan 3x \frac{1-2\sin 4x}{-1+2\sin 4x} = -\tan 3x.$$
