The oscillation results published by the Double Chooz collaboration in 2011 and 2012 rely on background models substantiated by reactor-on data. In this analysis, we present a background-model-independent measurement of the mixing angle $theta_{13}$ by including 7.53 days of reactor-off data. A global fit of the observed neutrino rates for different reactor power conditions is performed, yielding a measurement of both $theta_{13}$ and the total background rate. The results on the mixing angle are improved significantly by including the reactor-off data in the fit, as it provides a direct measurement of the total background rate. This reactor rate modulation analysis considers antineutrino candidates with neutron captures on both Gd and H, whose combination yields $sin^2(2theta_{13})=$ 0.102 $pm$ 0.028(stat.) $pm$ 0.033(syst.). The results presented in this study are fully consistent with the ones already published by Double Chooz, achieving a competitive precision. They provide, for the first time, a determination of $theta_{13}$ that does not depend on a background model.
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