Help With Negative Phases in a Numerical Term

[Blanchdog]

Homework Statement

Verify that $T^{tot}=\frac{n_2~cos \theta_2}{n_0~cos \theta_0}\frac{|t^{0\rightarrow1}|^2|t^{1\rightarrow2}|^2}{|e^{-ikd~cos\theta_1} - r^{0\leftarrow1}r^{1\rightarrow2}e^{ikd~cos\theta_1}|^2}$ simplifies to $T^{tot}=\frac{T^{max}}{1 + F~sin^2 \frac{\Phi}{2}}$ assuming all angles are real. Assume that all light is s polarized as the equations are precisely the same for p polarized light in terms of Fresnel coefficients.

Relevant Equations

Included in image below because I didn't want to have to LaTeX them all.

I think I've got the numerator part figured out, but I'm really stuck on what to do with those negative phases in the last term and how to get this to all come together in the end. I feel like I must have made a mistake somewhere, but can't find it. Thanks in advance for the help!

 

[Charles Link]

One error that I think I spotted is right by 4.14: In evaluating $|terms|^2$, you need to multiply "terms" by its complex conjugate.