What experiment(s), specifically tell you that a spin-1/2 particle has rotated one full rotation (360°), but is (in some other respect) only 'rotated' by 180°?
Or, conversely, if a spin-2 particle has gone through an alleged half-rotation, but is now (again, in some other, mysterious respect) back to where it started?
What is the difference between the 'phase' shift a particle goes through, versus its 'spin' shift?
