Double Layer Reflection

$$R=\left|r^2\right|=\frac{r_1^2+r_2^2+r_3^2+r_1^2{r}_2^2{r}_3^2+2r_1{r}_2\left(1+r_3^2\right)\cos 2{\theta }_1+2r_2{r}_3\left(1+r_1^2\right)\cos 2{\theta }_2+2r_1{r}_3\cos 2\left({\theta }_1+{\theta }_2\right)+2r_1{r}_2^2{r}_3\cos 2\left({\theta }_1-{\theta }_2\right)}{1+r_1^2{r}_2^2+r_1^2{r}_3^2+r_2^2{r}_3^2+2r_1{r}_2\left(1+r_3^2\right)\cos 2{\theta }_1+2r_2{r}_3\left(1+r_1^2\right)\cos 2\theta +2r_1{r}_3\cos 2\left({\theta }_1+{\theta }_2\right)+2r_1{r}_2^2{r}_3\cos 2\left({\theta }_1-{\theta }_2\right)}$$