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Measurements of neutral current Drell-Yan production at large invariant dilepton masses can be used to test the energy scale dependence (running) of the electroweak mixing angle. In this work, we make use of a novel implementation of the full next-to-leading order electroweak radiative corrections to the Drell-Yan process using the MS‾ renormalization scheme for the electroweak mixing angle. The potential of future analyses using proton-proton collisions at s=13.6TeV in the Run 3 and High-Luminosity phases of the LHC is explored. In this way, the Standard Model predictions for the MS‾ running at TeV scales can be probed.