Prove that cos a + cos 2a + cos 3a + cos 4a = 4 cos (a/2)cos a cos (5a/2)

i can prove this .

hence , find all the values of a between 0 and 180 such that

cos a + cos 2a + cos 3a + cos 4a =0

so i know i should start like this

4 cos (a/2)cos a cos (5a/2)=0

but i am unsure how to continue here .