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We develop a path-integral theory to calculate the angle-resolved photoemission spectra (ARPES) of high-Tc superconductors based on a two-dimensional model for the CuO2 conduction plane, which includes both electron-electron (e-e) and electron-phonon (e-ph) interactions. By making use of the Hubbard-Stratonovich transformation and the Gaussian integral formula, the two-body e-e and e-ph correlated terms are decoupled to a two-fold summation over the auxiliary spin and lattice configurations, which is the so-called path-integral and numerically performed by the quantum Monte Carlo simulation. In this way we calculate the ARPES on a nano-sized cluster, and compare the results with the experimental data of Bi2Sr2CaCu2O8. We find that, the experimentally observed anomalous isotopic shift in the ARPES of Bi2Sr2CaCu2O8 can be attributed to the phonon softening effect driven by the quadratic e-ph coupling. While the strong e-e correlation partially suppresses this isotopic shift. |