I haven't checked your numbers, but the first place I'd look would be at "R". The moon moves in an elliptical orbit around the Earth. Your formula seems to be about a circular orbit. Also, the moon is perturbed in that orbit somewhat, and has its perigee angle move around the ecliptic once every 18 or 19 years... and I believe because of the Sun's interaction, the moon does not follow a strictly elliptical orbit, but one that is squared out a little bit from that. Your calcualtion only deviates by 0.13% from the observed value.
You've chosen an interesting but complex topic. Hopefully someone with more depth of knowledge can tell you more specifically.
Forming opinions as we speak