Given:
[tex]cos(2\theta)sin(\theta)+sin(\theta)=0[/tex]
let us take the common term out,
[tex]\begin{gathered} sin(\theta)(cos(2\theta)+1)=0 \\ \end{gathered}[/tex]
Now, let us solve seperately,
[tex]\begin{gathered} \sin (\theta)=0 \\ \theta=2\pi n \end{gathered}[/tex]
[tex]\begin{gathered} \cos (2\theta)+1=0 \\ \theta=\frac{\pi}{2}+\pi n \end{gathered}[/tex]
The solutions are,
[tex]\theta=2\pi n,\: \theta=\pi+2\pi n,\: \theta=\frac{\pi}{2}+\pi n[/tex]
