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We investigated the nonlinear Meissner effect (NLME) in Nb3Sn thin film coplanar resonators by measuring the resonance frequency as a function of a dc magnetic field applied parallel to the film surface at different temperatures. We used low rf power probing in films thinner than the London penetration depth λ(B) to significantly increase the field onset of vortex penetration and measure the NLME under equilibrium conditions. Contrary to the quadratic increase of λ(B), expected in s-wave superconductors, we observed a nearly linear increase of the penetration depth with B. Theoretical analysis of our experimental data has shown that that the observed behavior of λ(B) does not result from the conventional dc current pairbreaking effects but results from weak linked grain boundaries which significantly increase the kinetic inductance of our polycrystalline Nb3Sn films.