Redshift-space distortions (RSD) offers an exciting opportunity to test the gravity on cosmological scales. In the presence of galaxy bias, however, the RSD measurement at large scales, where the linear theory prediction is safely applied, is known to exhibit a degeneracy between the parameters of structure growth f and fluctuation amplitude sigma8, and one can only constrain the parameters in the form of fsigma8. In order to disentangle this degeneracy, in this paper, we go beyond the linear theory, and consider the model of RSD applicable to a weakly nonlinear regime. Based on the Fisher matrix analysis, we show explicitly that the degeneracy of the parameter fsigma8 can be broken, and sigma8 is separately estimated in the presence of galaxy bias. Performing further the Markov chain Monte Carlo analysis, we verify that our model correctly reproduces the fiducial values of fsigma8 and sigma8, with the statistical errors consistent with those estimated from the Fisher matrix analysis. We show that upcoming galaxy survey of the stage-IV class can unambiguously determine sigma8 at the precision down to 10% at higher redshifts even if we restrict the accessible scales to k<0.16h/Mpc
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