  We present a theoretical study of the response of
$\beta$-$\text{Li}_2\text{IrO}_3$ under external magnetic fields in the $ab$,
$bc$ and $ac$ crystallographic planes. The results are based on the minimal
nearest-neighbor $J$-$K$-$\Gamma$ model and reveal a rich intertwining of
field-induced phases and magnetic phase transitions with distinctive signatures
that can be probed directly via torque magnetometry. Most saliently, we
observe: i) an unusual reentrance of the incommensurate counter-rotating order
for fields in the $ab$-plane, and ii) a set of abrupt torque discontinuities
which are particularly large for fields rotating in the $bc$ plane, and whose
characteristic shape resembles closely the ones observed in the 3D Kitaev
magnet $\gamma$-$\text{Li}_2\text{IrO}_3$. An experimental confirmation of
these predictions will pave the way for an accurate determination of all
relevant microscopic parameters of this 3D Kitaev magnet.
