One of my interests PENKO, the sky.
While there are equations you can muscle through on your own, try this Excel spreadsheet
http://www.ecy.wa.gov/programs/eap/models/twilight.zip Comes from a Washington state website and is bug-free.
Add 8 minutes for sunset times and subtract 8 for sunrise times at FL350-400.
UTM to Lat/Lon calculators are available, but I just use a simple UTM/Coordinate map.