The OPERA experiment has conclusively observed the appearance of tau neutrinos in the muon neutrino CNGS beam. Exploiting the OPERA detector capabilities, it was possible to isolate high purity samples of $ u_{e}$, $ u_{mu}$ and $ u_{tau}$ charged current weak neutrino interactions, as well as neutral current weak interactions. In this Letter, the full dataset is used for the first time to test the three-flavor neutrino oscillation model and to derive constraints on the existence of a light sterile neutrino within the framework of the $3+1$ neutrino model. For the first time, tau and electron neutrino appearance channels are jointly used to test the sterile neutrino hypothesis. A significant fraction of the sterile neutrino parameter space allowed by LSND and MiniBooNE experiments is excluded at 90% C.L. In particular, the best-fit values obtained by MiniBooNE combining neutrino and antineutrino data are excluded at 3.3 $sigma$ significance.
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