Use sumtoproduct formulas to find the solutions of the equat

Use sum-to-product formulas to find the solutions of the equation. (Use n as your arbitrary integer. Enter your answers as a comma-separated list.)

sin 5x ? sin x = 2 cos 3x

I understand how to get pin/3 + pi/6 but I don\'t understand how to get the other.

sin 5x sin x = 2 cos 3x

LHS : 2cos(3x)sin2x

2cos(3x)sin2x - 2 cos 3x =0

2cos3x( sin2x -1) =0

cos3x =0

3x = pi/2 + 2n*pi ; x= (pi + 4pi*n)/6

3x= 3pi/2 +2n*pi ; x= ( 3pi +3n*pi)/6

sin2x =1 ; 2x = pi/2 + 2n*pi

x = (pi + 4n*pi)/4