the angle of rotation would be 2pi/6 = pi/3, because if 6 rotations are needed for a full rotation (no net effect = identity), then 6 times the angle of rotation = 2pi.

I'm not sure about the axis of rotation though.

EDIT: nvm I messed up. what I said is only true if X^6 = X, not X^6 = I, however, if X^6 = I, then X^7 = X, which means the angle of rotation is (2pi)/7 for similar reasons described above