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The period-luminosity (PL) relation of Cepheids in the Large Magellanic Cloud(LMC) plays a pivotal role in extra-galactic distance measurement and thedetermination of the Hubble constant $(H_{0})$. In this work, we probe thegeometry of the LMC through a detailed study of multi-phase PL relations ofthese Cepheids, leveraging data from the OGLE-IV and Gaia DR3 databases. Weanalyse the light curves of a combined sample of $\sim$3300 fundamental (FU)and first overtone (FO) mode classical Cepheids. We obtain multi-phase datawith $50$ 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 thedistance modulus and reddening values of individual Cepheids by fitting asimultaneous reddening law to the apparent distance modulus values. Wecalculate the LMC viewing angle parameters: the inclination angle $(i)$ andposition angle of line of nodes $(\theta_{\rm lon})$ by fitting a plane of theform $z = f(x,y)$ to the three-dimensional distribution of Cepheids inCartesian coordinates $(x,y,z)$. The values of LMC viewing angles frommulti-phase PL relations are found to be: $i = 22\rlap{.}^{\circ}87 \pm0\rlap{.}^{\circ}43 ~\textrm{(stat.)} \pm 0\rlap{.}^{\circ}53~\textrm{(syst.)}$, $\theta_{\rm lon} = 154\rlap{.}^{\circ}76 \pm1\rlap{.}^{\circ}16 ~\textrm{(stat.)} \pm 1\rlap{.}^{\circ}01~\textrm{(syst.)}$, respectively. The use of multi-phase PL relations inmultiple bands results in lower uncertainties for the LMC viewing angleparameters as compared to those derived from the mean light PL relations. Thisshows that the use of multi-phase PL relations with multi-wavelength photometrysignificantly improves the precision of these measurements, allowing betterconstraints on the morphology and the structure of the LMC.

Geometry of the LMC based on multi-phase analysis of multi-wavelength Cepheid light curves using OGLE-IV and Gaia DR3 data