We have employed a magnetic field angle as a tuning parameter in a comprehensive measurement of the specific heat, magnetocaloric effect, and magnetization for the quasi-kagome Kondo lattice CeRhSn, which is considered to exhibit zero-field quantum criticality driven by geometrical frustration. By constructing the field-angle-resolved landscape of the entropy, we unexpectedly revealed that the non-Fermi-liquid nature survives up to a metamagnetic crossover field of roughly 3 T in the very narrow field-orientation range, close to the direction parallel to the quasi-kagome plane. We propose that spin fluctuations along the hexagonal $c$ axis are the dominant driving force for the non-Fermi-liquid behavior because it is strongly suppressed by a magnetic-field component along the $c$ axis. The multidimensional entropy landscape, which directly reflects the degeneracy of ground states, opens a new route for uncovering the nature of exotic phases in anisotropic systems.
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