I'll post up where I'm at with this. Perhaps you will see it before I do.
Let , .
I further simplified this by letting , .
Then we get...
However I can't advance past this yet! Perhaps you can.
Nice solution simplependulum.
This is what I further thought of at 4am!
EDIT: Apparently that minus should not be there (or there should be a minus in front of the ) but I can't figure out what I've done wrong after skimming over it.