[tex]2\cos\theta*\tan\theta + \tan\theta = 0
\\
\\2\cos\theta* \frac{\sin\theta}{\cos\theta} + \frac{\sin\theta}{\cos\theta} = 0
\\
\\ 2\sin\theta + \frac{\sin\theta}{\cos\theta} = 0
\\
\\ \frac{2\sin{\theta}\cos{\theta}}{\cos{\theta}} + \frac{\sin\theta}{\cos\theta} = 0
\\
\\ \frac{2\sin{\theta}\cos{\theta}+\sin{\theta}}{\cos{\theta}} =0
\\
\\ 2\sin{\theta}\cos{\theta}+\sin{\theta}=0
\\
\\ \sin\theta(2\cos\theta+1)=0
\\
\\ \sin\theta=0 \Rightarrow \theta=0, \pi,2\pi
\\
\\2\cos\theta=-1
\\
\\\cos\theta=- \frac{1}{2} \Rightarrow \theta= \frac{2\pi}{3} , \frac{4\pi}{3}
[/tex]
Therefore, [tex]\theta=0, \pi,2\pi ,\frac{2\pi}{3} , \frac{4\pi}{3}[/tex]
