Elliptic flow of hadrons observed at relativistic heavy ion collision experiments at relativistic heavy ion collider (RHIC) and large hadron collider (LHC) provides us an important signature of possible deconfinement transition from the hadronic phase to partonic phase. However, hadronization processes of deconfined partons back into final hadrons are found to play a vital role in the observed hadronic flow. In the present work, we use a coalescence mechanism also known as recombination (ReCo) to combine quarks into hadrons. To get there, we have used the Boltzmann transport equation in relaxation time approximation to transport the quarks into equilibration and finally to freeze-out the surface, before coalescence takes place. A Boltzmann-Gibbs blast wave (BGBW) function is taken as an equilibrium function to get the final distribution and a power-like function to describe the initial distributions of partons produced in heavy ion collisions. In the present work, we try to estimate the elliptic flow of identified hadrons such as $\pi$, $K$, and $p$, produced in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76\text{TeV}$ at the LHC for different centralities. The elliptic flow ($v_2$) of identified hadrons seems to be described quite well in the available $p_{\text{T}}$ range. After the evolution of quarks until freeze-out time has been calculated using BTE-RTA, the approach used in this paper consists of combining two or more quarks to explain the produced hadrons at intermediate momenta regions. The formalism is found to describe the elliptic flow of hadrons produced in Pb+Pb collisions to a large extent.