Determine overlaps of polar coordinate vectors

Hi, I need some help and hint for an algorithm, which can find the overlap covered by max. number of polar coordinates vectors (unit: degree). The difficult thing here is that the coordinate can "saturate" and take overturn. e.g. [355.9958 9.0903] and [2.55 10] share the area [9.0903 10].

Anyone has an idea? It has to be as fast as possible

e.g. with followiing polar coordinates in degree

316.1233  333.4349
298.3690  321.7830
320.1944  343.6518
301.3832  311.9872
356.9471    5.3322
251.7371  265.4261
334.9831  356.9471
139.6355  161.2220
169.7960  191.3099
232.0458  265.4261
320.6595  336.7323
246.2505  271.1458
356.5664   26.1049
328.9348  339.6955
355.9958    9.0903
329.2373  335.7723
10.7580   32.2109
262.0304  283.4957
327.0023  332.7305