4. Given $\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma=1, \alpha, \beta, \gamma$ are all acute angles, then the maximum value of $\cos \alpha \cos \beta \cos \gamma$ is
4. $\frac{2 \sqrt{6}}{9} \quad \cos \alpha \cos \beta \cos \gamma=\sqrt{\cos ^{2} \alpha \cdot \cos ^{2} \beta \cdot \cos ^{2} \gamma} \leqslant \sqrt{\left(\frac{\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma}{3}\right)^{3}}=\frac{2 \sqrt{6}}{9}$

4. $\frac{2 \sqrt{6}}{9} \quad \cos \alpha \cos \beta \cos \gamma=\sqrt{\cos ^{2} \alpha \cdot \cos ^{2} \beta \cdot \cos ^{2} \gamma} \leqslant \sqrt{\left(\frac{\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma}{3}\right)^{3}}=\frac{2 \sqrt{6}}{9}$