Keith -
I think you have a typo to correct. The sum becomes greater (I think the limit is probably 360o).
SK
Indeed. I started this to contradict you, and realized you were right. Keith is correct that the amount you turn is less, but that is because the amount you turn is the compliment of the angle that you measure on the triangle.
Visualize this maneuver: do a right-angle turn, as if to start a wingover. At the peak of the circle, do another right angle turn. Now do a right angle turn again, to recover level at 5 feet. Tra-la -- you have just done an equilateral triangle, with three 90 degree corners -- that adds up to 270 degrees.
Where Keith is right is that on a flat surface, the equilateral triangle requires you to turn thrice at 120 degrees, for a total of 360; in my 90-degree example you must turn thrice at 90 degrees, or only 270 degrees.
For the degenerate case (put away those whips and the leather underwear -- I mean
mathematically degenerate) fly a level lap. When you pass your flight box say "turn", but stay level. Now fly 1/3 of the way around the circle and say "turn" again, but fly level. Now "turn" again at the 2/3 point. Congratulations! You have just inscribed the largest equalateral triangle that you can on the surface of a sphere. All the angles were 180 degrees, which meant that you only had to turn zero degrees.