  We developed a new technique for measuring the thermodynamic entropy as a
function of the magnetic field angle. This technique enables high-resolution
angle-resolved measurements of the entropy in an unprecedentedly short
measuring time. When the magnetic field is rotated under adiabatic conditions,
the sample temperature changes owing to the field-angle variation of its
entropy, which is referred to as the rotational magnetocaloric effect. By
investigating this effect along with the specific heat, the field-angle
dependence of the entropy can be determined. To demonstrate this technique, we
chose the spin-ice compound Dy$_2$Ti$_2$O$_7$ as a benchmark and showed good
agreement between the measured and theoretical entropies as a function of the
field angle. This development provides a new approach to studying
condensed-matter physics, in which multiple degrees of freedom play an
important role.
