Trigonometric cond identity

[ins-]

I would like to ask you how to prove the following conditional identity:

If $A,B,C,D,E >0$ and $A+B+C+D+E=180$
Then:
$\sin B\sin C[\sin(B+C)\sin(E+C) - \sin(A+D)\sin C] =\\ \sin A\sin E[\sin(A+E)\sin(E+C)-\sin(B+D)\sin E]$

(All the anges are in degrees)

[ins-]

I'm sorry it is not true. But if A,B,C,D,E are the angles of an inscribed pentagram it probably is true.