Question 116
Let $\alpha$, $\beta$ and $\gamma$ be three angles with $0 \leq \alpha, \beta, \gamma \lt 90^\circ$ and $\sin \alpha + \sin \beta + \sin \gamma = 1$. Show that
$$
\tan^2 \alpha + \tan^2 \beta + \tan^2 \gamma \geq \frac{3}{8}
$$
$$
\tan^2 \alpha + \tan^2 \beta + \tan^2 \gamma \geq \frac{3}{8}
$$