  Coherent and anticoherent states of spin systems up to spin j=2 are known to
be optimal in order to detect rotations by a known angle but unknown rotation
axis. These optimal quantum rotosensors are characterized by minimal fidelity,
given by the overlap of a state before and after a rotation, averaged over all
directions in space. We calculate a closed-form expression for the average
fidelity in terms of anticoherent measures, valid for arbitrary values of the
quantum number j. We identify optimal rotosensors (i) for arbitrary rotation
angles in the case of spin quantum numbers up to j=7/2 and (ii) for small
rotation angles in the case of spin quantum numbers up to j=5. The closed-form
expression we derive allows us to explain the central role of anticoherence
measures in the problem of optimal detection of rotation angles for arbitrary
values of j.
