Probability Density for Interferometer

[Einstein2nd]

Hey guys. All of the info for the problem is in a picture (sorry for not using the template).

I've tried working on this for ours and I still can't seem to get the trig identities right :(

http://img208.imageshack.us/img208/1770/assignmentquestion2.jpg

NOTE THAT THERE SHOULD BE ANOTHER BRACKET ON THE VERY END OF THE EQUATION FOR THE PROBABILITY DENSITY. IT SHOULD HAVE sin(delta)), NOT sin(delta) AS IT CURRENTLY HAS.

from that final step, I've done many things by both hand and scientific notebook and I just can't seem to get things to simplify down properly. There is no way I could possibly post all of the different things I've tried but don't worry, I'm not simply looking for a copy-paste answer into homework. I want to be able to understand the working.

Please clarify my initial working and steer me in the correct direction. I'm pretty sure that I understand the physics, it's just the maths...

 

[Einstein2nd]

Any chance of some help?

I was told to use Euler's formula (which I have tried in the past) and then separate the real and imaginary parts and then add the squares. I'm not getting the answer correct thoguh by doing this :(