  The period-luminosity (PL) relation of Cepheids in the Large Magellanic Cloud
(LMC) plays a pivotal role in extra-galactic distance measurement and the
determination of the Hubble constant $(H_{0})$. In this work, we probe the
geometry of the LMC through a detailed study of multi-phase PL relations of
these Cepheids, leveraging data from the OGLE-IV and Gaia DR3 databases. We
analyse the light curves of a combined sample of $\sim$3300 fundamental (FU)
and first overtone (FO) mode classical Cepheids. We obtain multi-phase data
with $50$ phase points over a complete pulsation cycle from the OGLE $(V, I)$
and Gaia $(G,G_{\rm BP}, G_{\rm RP})$ photometric bands. We determine the
distance modulus and reddening values of individual Cepheids by fitting a
simultaneous reddening law to the apparent distance modulus values. We
calculate the LMC viewing angle parameters: the inclination angle $(i)$ and
position angle of line of nodes $(\theta_{\rm lon})$ by fitting a plane of the
form $z = f(x,y)$ to the three-dimensional distribution of Cepheids in
Cartesian coordinates $(x,y,z)$. The values of LMC viewing angles from
multi-phase PL relations are found to be: $i = 22\rlap{.}^{\circ}87 \pm
0\rlap{.}^{\circ}43 ~\textrm{(stat.)} \pm 0\rlap{.}^{\circ}53
~\textrm{(syst.)}$, $\theta_{\rm lon} = 154\rlap{.}^{\circ}76 \pm
1\rlap{.}^{\circ}16 ~\textrm{(stat.)} \pm 1\rlap{.}^{\circ}01
~\textrm{(syst.)}$, respectively. The use of multi-phase PL relations in
multiple bands results in lower uncertainties for the LMC viewing angle
parameters as compared to those derived from the mean light PL relations. This
shows that the use of multi-phase PL relations with multi-wavelength photometry
significantly improves the precision of these measurements, allowing better
constraints on the morphology and the structure of the LMC.
