You hsve a cycle of 21 days, working 7, so 1/3 of the time. There are 365 days in a year.
365/3 = 121 2/3, meaning 121 days plus 2 extra, since you'd be back to working 3 days of the next 10, and the third day would be the first day of the next year.
Soooooo, 123 days.