  $\alpha$-RuCl$_3$ is a promising candidate material to realize the so far
elusive quantum spin liquid ground state. However, at low temperatures, the
coexistence of different exchange interactions couple the effective pseudospins
into an antiferromagnetically zigzag (ZZ) ordered state. The low-field
evolution of spin structure is still a matter of debate and the magnetic
anisotropy within the honeycomb planes is an open and challenging question.
Here, we investigate the evolution of the ZZ order parameter by second-order
magneto-optical effects, the magnetic linear dichroism and magnetic linear
birefringence. Our results clarify the presence and nature of metamagnetic
transitions in the ZZ phase of $\alpha$-RuCl$_3$. Our experimental observations
show the presence of initial magnetic domain repopulation followed by a
spin-flop transition for small in-plane applied magnetic fields ($\approx$ 1.6
T) along specific crystallographic directions. In addition, using a
magneto-optical approach, we detected the recently reported emergence of a
field-induced intermediate phase before suppressing the ZZ order. Our results
disclose the details of various angle-dependent in-plane metamagnetic
transitions quantifying the bond-anisotropic interactions present in
$\alpha$-RuCl$_3$
