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