3. Given $\frac{\sin (\beta+\gamma) \sin (\gamma+\alpha)}{\cos \alpha \cos \gamma}=\frac{4}{9}$, then the value of $\frac{\sin (\beta+\gamma) \sin (\gamma+\alpha)}{\cos (\alpha+\beta+\gamma) \cos \gamma}$ is $\qquad$ .
3. $\frac{4}{5}$.