Here is an appraoch using genfit to find the sinusoidal fit.
Personally, I never use genfit. I find minerr easier to set up for anything other than very simple fits, and much more versatile.
I guess using FFT could do the job, too.
Not with much accuracy, because the data does not have an integer number of periods, and the number of periods is small. However, I have found in the past that a least squares fit of a sinusoid can be very sensitive to the guesses (especially if the sinusoid is undersampled), in which case an FFT is a great way of getting starting guesses. Some years ago I posted a worksheet that uses this approach. See http://communities.ptc.com/message/134317#134317