Equations in sin²θ, cos²θ, tan²θ

Ravi solves $\tan^2\theta = \frac{1}{3}$ as $\tan\theta = \frac{1}{\sqrt{3}}$, so $\theta = n\pi + \frac{\pi}{6}$. Is $\theta = \frac{5\pi}{6}$ a solution he missed?