Question: Simplification of trigonometric equations. VI

Hello,

I would like to simplify a trigonometric equation that I obtain with a vectorial closure (in mechanics)

Here the equation that I would like to simplify 

eq_liaison :=(-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*l2[1]+((-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*cos(th(t))+(-cos(p(t)+g(t))*cos(a(t))+sin(a(t))*sin(b(t))*sin(p(t)+g(t)))*sin(th(t)))*l3[1] = 0

Do you have ideas so as to simplify again this expression ?

This expression can still be simplified. You can find here the result expected :

I find surprising that I have so many difficulties to make trigonometric simplications with the trigonometric functions.

Thank you for your help

PS : Sorry for duplicating posts. As I didn't receive any answer, I have tried to simplified my post to isolate the difficulty.