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We present a soft x-ray angle-resolved photoemission spectroscopy study of overdoped high-temperature superconductors. In-plane and out-of-plane components of the Fermi surface are mapped by varying the photoemission angle and the incident photon energy. No kz dispersion is observed along the nodal direction, whereas a significant antinodal kz dispersion is identified for La-based cuprates. Based on a tight-binding parametrization, we discuss the implications for the density of states near the van Hove singularity. Our results suggest that the large electronic specific heat found in overdoped La2-xSrxCuO4 cannot be assigned to the van Hove singularity alone. We therefore propose quantum criticality induced by a collapsing pseudogap phase as a plausible explanation for observed enhancement of electronic specific heat.