Transverse momentum dependent parton distributions (TMDs) are an important class of functions required to understand the 3D structure of hadrons in terms of their underlying partons. One of the least known TMDs in terms of a global QCD analysis is the worm-gear TMD $g_{1T}$. It carries the probabilistic interpretation of finding longitudinally polarized quarks inside transversely polarized hadrons. In this proceedings, we present the first-ever global QCD analysis of the semi-inclusive DIS $A^{\textrm{cos}(\phi_{h} -\phi_{S})}_{LT}$ data using Monte Carlo techniques to extract the worm-gear TMD $g_{1T}$. The relevant data are available from COMPASS, HERMES and JLab. We compare our results for $g_{1T}$ with different theoretical approaches, including the large-$N_c$ approximation, the Wandzura-Wilczek-type approximation, and lattice QCD.