  A comprehensive study of magnetocrystalline anisotropy of a layered
van-der-Waals ferromagnet VI3 was performed. We measured angular dependences of
the torque and magnetization with respect to the direction of the applied
magnetic field within the "ac" plane perpendicular to and within the basal ab
plane, respectively. A two-fold butterfly-like signal was detected by
magnetization in the perpendicular "ac" plane. This signal symmetry remains
conserved throughout all magnetic regimes as well as through the known
structural transition down to the lowest temperatures. The maximum of the
magnetization signal and the resulting magnetization easy axis is significantly
tilted from the principal c axis by ~40{\deg}. The close relation of the
magnetocrystalline anisotropy to the crystal structure was documented. In
contrast, a two-fold-like angular signal was detected in the paramagnetic
region within the ab plane in the monoclinic phase, which transforms into a
six-fold-like signal below the Curie temperature TC. With further cooling,
another six-fold-like signal with an angular shift of ~30{\deg} grows
approaching TFM. Below TFM, in the triclinic phase, the original six-fold-like
signal vanishes, being replaced by a secondary six-fold-like signal with an
angular shift of ~30{\deg}.
