Help With Negative Phases in a Numerical Term

Blanchdog
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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.
Finesse attempt pt 1.png

Finesse attempt pt2.png

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!
 
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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.
 

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