Yes, I see I have mis-stated the coincident times a bit. I did mean minutes after 3:15, 4:20, 5:25 etc.
Each time the minute and hour hands are coincident, the second hand is at 12:00. And by the time it has moved to where the minute and hour time are, they are no longer coincident. The one time when all three are coincident is during the 11:00 hour, when the minute and hour hand and second hand are just moving past 11:59:59. Here they will all be coincident at 12:00:00. That may be the only time when all are lined up, but I am not sure.