[tex]tan (2 \theta)+tan \theta = \frac{2 tan \theta}{1-tan^2 \theta} +tan \theta = 0[/tex]
Multiplying equation by denominator gives:
[tex]2 tan \theta + tan \theta (1-tan^2 \theta) = 0[/tex]
Factor out a tan
[tex]tan \theta (3-tan^2 \theta) = 0 \\ tan\theta = 0, \pm \sqrt{3}[/tex]
[tex]\theta = 0, \frac{\pi}{3}, \frac{2\pi}{3} [/tex]
