Sea $0 \leq \alpha , \beta , \gamma \leq \frac{\pi}{2}$, tal que $\cos ^{2} \alpha + \cos ^{2} \beta + \cos ^{2} \gamma = 1$. Demuestre que $2 \leq (1 + \cos ^{2} \alpha ) ^{2} \sin^{4} \alpha + (1 + \cos ^{2} \beta ) ^{2} \sin ^{4} \beta + (1 + \cos ^{2} \gamma ) ^{2} \sin ^{4} \gamma \leq (1 + \cos ^{2} \alpha )(1 + \cos ^{2} \beta)(1 + \cos ^{2} \gamma ).$