Sin(x)-sin(3x)=sin(4x)-sin(2x)

sin(x) - sin(4x) = sin(3x) - sin(2x)

-2cos(5x/2)sin(3x/2) = 2cos(5x/2)sin(x/2)

-cos(5x/2)sin(3x/2) = cos(5x/2)sin(x/2)

-sin(3x/2) = sin(x/2)

-(sin(3x/2) + sin(x/2)) = 0

sin(3x/2) + sin(x/2) = 0

2sin(x)cos(x/2) = 0

x = (-1)ⁿarcsin(0) + πn, n ∈ Z

x = πn, n ∈ Z

x/2 = arccos0 + πn, n ∈ Z

x = π + 2πn, n ∈ Z