Sinx+sin2x+sin3x+sin4x=0
(sinx+sin4x)+(sin2x+sin3x)=0
2sin(5x/2)cos(3x/2)+2sin(5x/2)cos(x/2)=0|:2
sin(5x/2)(cos(3x/2)+cos(x/2))=0
sin(5x/2)*2cos(x)*cos(x/2)=0
1) sin(5x/2)=0
5x/2=πn
x=(2πn)/5,n∈Z.
2) cosx=0
x=(π/2)+πn,n∈Z.
3) cos(x/2)=0
x/2=(π/2)+πn
x=π+2πn,n∈Z.