  We report an experiment estimating the three parameters of a general
rotation. The scheme uses quantum states attaining the ultimate precision
dictated by the quantum Cram\'er-Rao bound. We realize the states
experimentally using the orbital angular momentum of light and implement the
rotations with a multiplane light conversion setup, which allows one to perform
arbitrary unitary transformations on a finite set of spatial modes. The
observed performance suggests a range of potential applications in the next
generation of rotation sensors.
