If you fly over the pole you basically cover 180 degrees of longitude, and it matters little whether you take the 180 that cross the date line or the 180 degree

If you fly over the pole you basically cover 180 degrees of longitude, and it matters little whether you take the 180 that cross the date line or the 180 degrees that don't. Crossing the date line is just an artifact of the singularity at the pole.