Find the exact solutions of the equation in the interval 02p

Find the exact solutions of the equation in the interval [0,2pi) enter your answers as a comma separated list

Sin 2x + sin x =0

sin2x + sinx =0

use the trig identity : sin2x = 2sinxcosx

2sinxcosx +sinx =0

sinx( 2cosx+1) =0

sinx =0

x= 0, pi in the interval [0,2pi )

cosx = -1/2

x= pi -pi/3 , pi +pi/3 (cos is -ve in IInd and IIIrd quadrant)

x = 2pi/3, 4pi/3

Solution : x = 0, pi , 2pi/3 , 4pi/3