(Edit: don't bother with the formulas below-- I forgot you probably want normal-section azimuth which is much simpler. I'll look that one up and get back to you.)
See if this one is any use to you
http://www.ferris.edu/FACULTY/BURTCH...ct-inverse.pdf
That's the up-to-100+ km formula. If you want to work on it let me know-- it might need a bit of clarification.
The long-distance formulas are at
http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
Those may not be the best any more, but the improved formulas aren't on line
AFAIK. In any case it does the job.
I was assuming you wanted something more accurate than you'd get by assuming the earth was a sphere, but of course those formulas are much simpler still.