I don't math good. I've been trying to come up with a calendar for a colony on Titan. I assume that any colonists would employ three calendars: a native calendar set to the rhythms of their own world; a common, utilitarian calendar used for communication between worlds, and the native Earth calendar. The common calendar would be a simple count of 360 24-hour days, with no regard for months or weeks.

This native calendar, the "long calendar", would be of very little practical use, mainly used for timing native seasonal celerations, such as the coming of the winter rains, and the Great White Spot.

The Saturnian year consists of 674.770774537 Titanian days. What is the pattern of leap days required to keep pace with the seasons, assuming a 675-day calendar?