I’m no scientist, but did study the 12 perturbations of Earth’s motion in an astronomy class in college. My gut instinct is that if you take all the perturbations collectively there will be some harmonic relationship that causes this. In other words, all the perturbations have some effect on the others and eventually this harmonic situation maybe could arise from this.
The different forces at work are mostly just the Moon and Sun. The Moon produces 2/3rds of the tides, the Sun the other 1/3rd; the Sun also beams energy at one side of the Earth at a time. The Earth’s motion through space is a bit of a double twist, as its axial tilt changes throughout the annual orbit around the Sun, and the lunar orbit crosses the axis at a different place each day thanks to the month (both synodic and sidereal) not being evenly divisible into the year.