Hey more of a comment, but the reason why phase shift loop works with key frames 2*pi, 4*pi, etc is the exact same reason why setting key frames at 360, 720 works. The units are just using radians instead of degrees. So you don't actually care about positive multiples of pi, you care about multiples of 2*pi, meaning -2*pi works the same as -360 from the other examples.
Yes cchabi-fin
Check out the previous comment...
great-tutorial-phase-offset
indeed, the phase seems to follow a sine or cosine function which has the same value at 2xpi intervals. You should be able to loop from any value by adding 2xpi to it or a multiple of 2xpi.