Sin4x + sinx = sin3x + sin2x

[latex]sin4x+sinx=sin3x+sin2x \\ 2* sin\frac{4x+x}{2}*cos \frac{4x-x}{2} =2*sin \frac{3x+2x}{2}*cos \frac{3x-2x}{2} \\ sin 2,5x*cos1,5x = sin2,5x*cos0,5x \\ cos1,5x=cos0,5x \\ x= \pi*n [/latex] n∈Z