If x sin a+y sin 2 a+z sin 3 a=sin 4 a, x sin b+y sin 2 b+z sin 3 b=sin 4 b, x sin c+y sin 2 c+z ...

If x sin a+y sin 2 a+z sin 3 a=sin 4 a,
x sin b+y sin 2 b+z sin 3 b=sin 4 b,
x sin c+y sin 2 c+z sin 3 c=sin 4 c,
then the roots of the equation
t^3-(z/2) t^2-(y+2/4) t+(z-x/8)=0
a, b, c ≠ n π, are
(1) sin a, sin b, sin c
(2) cos a, cos b, cos c
(3) sin 2 a, sin 2 b, sin 2 c
(4) cos 2 a, cos 2 b cos 2 c

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