Do the three hands on an analog clock (hours, minutes, seconds) ever divide the face of the clock into three equal segments, i.e. 120 degrees between each hand?
What about 8:20 or 4:40? I don't have any fancy computer programs, but it seems to me if the hour hand was on the 4, the minute hand was on the 8, and the second hand was on the 12, that would work. Same idea for 8:20, but switch the hour and minute hands.