Answer:
[tex]\frac{2\pi}{3}, \: \: \frac{5\pi}{3}[/tex]
Step-by-step explanation:
[tex] \tan \theta = - \sqrt{3} \\ \\ \implies \tan \theta = - \tan \frac{\pi}{3} \\ \\ \implies \: \tan \theta = \tan \bigg(\pi - \frac{\pi}{3} \bigg) \\ \\\implies \: \tan \theta = \tan \bigg(\frac{3\pi - \pi}{3} \bigg)\\ \\\implies \: \tan \theta = \tan \bigg(\frac{2\pi}{3} \bigg)\\ \\\implies \huge \red{\theta = \frac{2\pi}{3}} \\ \\ \\ \tan \theta = - \sqrt{3} \\ \\ \implies \tan \theta = - \tan \frac{\pi}{3} \\ \\ \implies \: \tan \theta = \tan \bigg(2\pi - \frac{\pi}{3} \bigg) \\ \\\implies \: \tan \theta = \tan \bigg(\frac{6\pi - \pi}{3} \bigg)\\ \\\implies \: \tan \theta = \tan \bigg(\frac{5\pi}{3} \bigg)\\ \\\implies \huge \orange{\theta = \frac{5\pi}{3}} \\ \\ \huge \: \purple { \boxed { \bold\theta = \frac{2\pi}{3}, \: \: \frac{5\pi}{3} }}[/tex]
