$\sin 2a + \sin 2b + \sin 2c - \sin 2(a+b+c) = 4 \sin (a+b) \sin (b+c) \sin (c+a)$ I am clueless about this homework question. Looking at it, I see I could use the compound angle and and sum formulas, and tried using them. Unfortunately, couldn't proceed beyond that. Help?
$$\sin 2a + \sin 2b + \sin 2c - \sin 2(a+b+c) = 4 \sin (a+b) \sin (b+c) \sin (c+a)$$

Using Prosthaphaeresis Formulas,
$$\sin2A+\sin2B=2\sin(A+B)\cos(A-B)$$
and $$\sin(2A+2B+2C)-\sin2C=2\sin(A+B)\cos(A+B+2C)$$
Finally,
$$\cos(A-B)-\cos(A+B+2C)=2\sin(A+C)\sin(B+C)$$
