posted by Anonymous .
the general solution of
sin x + sin 2x + sin 3x + sin 4x = 0 ?
obviously any multiple of pi/2 will work
sin pi/5 = sin 4pi/5 = 1/√8 (5-√5)
sin 2pi/5 = sin 3pi/5 = 1/√8 (5+√5)
any multiple of pi/5 will also work.
x = pi(n/2)
x = pi(2n/5)