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Got the Answer

Sort the interval start and end values into a single list with a corresponding value for 'S' or 'E' for each one.

Scan the list, when you hit an S increment a counter, when you hit an E decrement a counter. If the counter is higher than the highest value seen so far remember the S and E values for that segment.

For the wrap-around case, simply split each interval that wraps (i.e. angle2 < angle1) into two pieces, one either side of zero. Add [angle1,360] and [0,angle2] as new intervals into the starting set.