This paper addresses the impact of cubic nonlinearity on the operation of a rate-integrating gyroscope (RIG). It is demonstrated that below the bifurcation threshold, cubic nonlinearity results in angle-dependent frequency split between the two resonant modes of the gyroscope, which impacts angle-dependent bias, quadrature error, and controller efficacy in addition to distorting the scale factor due to off-resonant excitation. These errors are experimentally demonstrated using a high-Q disk resonator gyroscope, which are shown to be in close agreement with theory. A method of compensating for angle-dependent frequency error is proposed and experimentally validated. It is demonstrated that mode mismatch can be experimentally reduced to the level of thermal noise, effectively cancelling the effects of nonlinearity and eliminating the distortion of readout angle.