  Some, if not all, binary neutron star (BNS) coalescences, and a fraction of
neutron - star black hole (NSBH) mergers, are thought to produce sufficient
mass-ejection to power Gamma-Ray Bursts (GRBs). However, this fraction, as well
as the distribution of beaming angles of BNS-associated GRBs, are poorly
constrained from observation. Recent work applied machine learning tools to
analyze GRB light curves observed by {\textit{Fermi}}/GBM and {\it Swift}/BAT.
GRBs were segregated into multiple distinct clusters, with the tantalizing
possibility that one of them (BNS cluster) could be associated with BNSs and
another (NSBH cluster) with NSBHs. As a proof of principle, assuming that all
GRBs detected by {\it Fermi}/GBM and {\it Swift}/BAT associated with BNSs
(NSBHs) lie in the BNS (NSBH) cluster, we estimate their rates
($\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$). We compare these rates with
corresponding BNS and NSBH rates estimated by the LIGO-Virgo-Kagra (LVK)
collaboration from the first three observing runs (O1, O2, O3). We find that
the BNS rates are consistent with LVK's rate estimates, assuming a uniform
distribution of beaming fractions ($f_b \in [0.01, 0.1]$). Conversely, using
the LVK's BNS rate estimates, assuming all BNS mergers produce GRBs, we are
able to constrain the beaming angle distribution to $\theta_j \in [0.8^{\circ},
38.8^{\circ}]$ at $90\%$ confidence. We similarly place a lower limit on the
fraction of GRB-Bright NSBHs to $f_B \gtrsim 0.10$ ($f_B \gtrsim 0.022$) with
{\it Fermi}/GBM ({\it Swift}/BAT) data.
