First factor out a sin(x)
[tex]sin x (1 + 2cos x) = 0[/tex]
Now you can split it into factors, where each factor = 0 and solve them separately.
[tex]sin x = 0 , 1 + 2cos x = 0[/tex]
[tex]sin x = 0 , cos x = -\frac{1}{2}[/tex]
You can use the unit circle to find the appropriate angles:(attached)
sin x = 0 when
[tex]x = 0, \pi [/tex]
cos x = -1/2 when
[tex]x = \frac{2 \pi }{3}, \frac{4 \pi }{3} [/tex]
