If a+b+c=180° then prof that sin 2a + sin 2b + sin 2c = 4cos a cos b sin c

Dear Student,
Let me first correct your question, It should be
sin 2a + sin 2b – sin 2c = 4 cos a cos b sin c or
sin 2a + sin 2b – sin 2c = 4 sin a sin b sin c
and to prove either of this, simple apply the formula in LHS part sin A + sin B = 2 sin (A+B)/2 cos (A-B)/2 and also you a+b = 180 -c or b+c = 180-a or a+c = 180-b.
I hope you will get the end result.
Thanks.