I have "This rock on the horizon is where the evil yellow ball comes up over" ironed into my skull, but you may wish to try this website which gives position of the sun/moon at different times of day based on your location.
http://aa.usno.navy.mil/data/docs/AltAz.html
You will also need the time of sunrise/sunset to fill out this form:
http://aa.usno.navy.mil/data/docs/RS_OneDay.html
The playa is roughly at 40 42.018 N 119 14.661 W
That's actually a site about 4 miles to the east of burning man on the jungo road that I keep loaded into my GPS, but the difference will be lower than you can measure with your compass.
You may want to be careful about the whole daylight savings time thing or your calculations could be off by as much as 10 degrees. I don't know if that matters for what you want.
Um, increase self-reliance? With an astronomy textbook you can calculate this from first principles. I'd advise not basing the success of your playa experience on more than 5 degree accuracy in sunrise/sunset. Sunrise and sunset aren't 180 deg away from eachother, but if you stare at the sun closely enough to figure this out, you'll probably regret it.