  We evaluate the entanglement entropy of a non-minimal coupling
Einstein-scalar theory with two approaches in classical Euclidean gravity. By
analysing the equation of motion, we find that the entangled surface is
restricted to be a minimal surface. The entanglement entropy formula is derived
directly from the approach of regularized conical singularity. On the other
hand, by expressing Ricci scalar of the conical spacetime, we obtain the same
result. In addition, we generalize the reduced geometric approach to Riemann
tensor and its derivations.
