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A measurement of the \({t\overline{t}}Z\) and \({t\overline{t}}W\) production cross sections in final states with either two same-charge muons, or three or four leptons (electrons or muons) is presented. The analysis uses a data sample of proton–proton collisions at \(\sqrt{s}\) = 13 TeV recorded with the ATLAS detector at the Large Hadron Collider in 2015, corresponding to a total integrated luminosity of 3.2 fb\(^{−1}\). The inclusive cross sections are extracted using likelihood fits to signal and control regions, resulting in \(\sigma_{{t\overline{t}}Z}\) = 0.9 ± 0.3 pb and \(\sigma_{{t\overline{t}}W}\) = 1.5 ± 0.8 pb, in agreement with the Standard Model predictions.