A rotation axis which makes the same angle with the x, y, and z axis (of a cartesian coordinate system) will be at the magic angle (54.7356 degrees) from each of the axes. A 120 degree rotation about that axis will move the z-axis onto the x-axis, the x-axis onto the y-axis, and the y-axis onto the z-axis.
If the sample is spun rapidly (compared to the changes in the NMR frequency which occur during sample rotation) the orientational dependence averages. For typical solids, the spinning rate should be 1 kHz or higher. If the sample is spun at a slower rate, the time dependence of the NMR frequency (e.g. frequency modulation) yields a spectrum containing sidebands. The spacing between the sidebands is equal to the spinning rate.
Some interactions, such as those from electric quadrupole fields, do not average completely upon rotation. In addition, if the rotation is not at the magic angle, the averaging of all the interactions will not be complete.
Reference: Journal of Magnetic Resonance A120, 88-96 (1996).