Hi, I'm struggling with this question:

Show that

$\displaystyle 4sin(\alpha + \beta)sin(\alpha + \gamma)sin(\beta + \gamma) + sin(2\alpha + 2\beta + 2\gamma) = sin(2\alpha) + sin(2\beta) + sin(2\gamma)$

I have covered identities but I get in a huge expansion that is so confusing and from past questions tend to have a neater way of doing things.

Your help would be greatly appreciated.

D