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4 on 2 off = 4/6 = 2/3 days worked ⇒ 2/3 x 365 days ≈ 243 (or 244) days per year.
An event occurs 2 times in a year
if it's not a leap year, the answer is 427 days
If neither years is a leap year, 735 days = 2 years, 5 days. If either is a leap year, it is 2 years, 4 days.