  In this work we derive a new scheme to calculate Tomonaga-Luttinger liquid
(TLL) parameters and holon (charge modes) velocities in a quasi-1D material
that consists of two-leg ladders coupled through Coulomb interactions. Firstly,
we obtain an analytic formula for electron-electron interaction potential along
the conducting axis for a generalized charge distribution in a plane
perpendicular to it. In the second step we introduce many-body screening that
is present in a quasi-1D material. To this end we propose a new approximation
for the charge susceptibility. Based on this we are able to find the TLL's
parameters and velocities. We then show how to use these to validate the
experimental ARPES data measured recently in p-polarization in $NbSe_3$.
Although we focus our study on this specific material it is applicable for any
quasi-1D system that consists of two-leg ladders as basic units.
