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sinx+siny+sinz=0
then what is sin3x+sin3y+sin3z=
sin3A = 3sinA - 4sin3A, x3+y3= (x+y)(x2-xy+y2)
sin3x +sin3y +sin3z= 3(sinx+siny+sinz)-4(sin3x+sin3y+sin3z) = -4((sinx+siny)3 -3sinxsiny(sinx+siny)+sin3z)
=-4((sinx+siny+sinz)((sinx+siny)2 +sin2z -sinz(sinx+siny)) +12sinxsiny(sinx+siny)=-12sinxsinysinz
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