Sea $0 < \alpha, \beta, \gamma < \frac{\pi}{2}$ y $\sin^{3} \alpha + \sin^{3} \beta + \sin^3 \gamma = 1$ . Demuestre que\n\[ \tan^{2} \alpha + \tan^{2} \beta + \tan^{2} \gamma \geq \frac{3 \sqrt{3}}{2} . \]