Solve sin A + sin 2A + sin 3A + sin 4A = 0, for 0 < A < 180 (0 and 180 inclusive)

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Solve sin A + sin 2A + sin 3A + sin 4A = 0, for 0 < A < 180 (0 and 180 inclusive)

Mathematics
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I've tried using factor formula but still did not manage to get the answer, not sure if factor formula is the right method
I rearrange to sin 4A + sin 2A + sin 3A + sin A = 0, and after applying factor formula, 2 sin 3A cos A + 2 sin 2A cos A = 0 2 cos A ( sin 3A + sin 2A) = 0 2 cos A ( sin 5/2 A cos 1/2 A) = 0

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Other answers:

\(A=0^{\circ}\) is one solution by obsrvation
@HatcrewS you are on the right road to solving it
@welshfella how do I continue from there ? T.T
i think there is an error in your last line
2 cos A ( sin 5/2 A cos 1/2 A) = 0 should be 2 cos A ( 2 sin 5/2 A cos 1/2 A) = 0 now its just a matter of equating the 3 terms to 0
@welshfella oh okay i'll try again thanks!
2 cos A = 0 A = 90 degrees
I solve and got 0, 90, 144, 180 but im still missing 72(answer sheet shows that 72 is one of the answer). Can someone help me get 72 ?

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