Last decades are marked with widespread interest to spin-related phenomena in semiconductor nanostructures. Experimetnal approach based on Faraday and Kerr rotation technique allows one to obtain easily detectable signals, of the order of mrad, even from nanometer-sized objects. In this work we report a record value of the Kerr rotation angle observed in a series of pump-probe optically induced Kerr rotation experiments of a semiconductor quantum well microcavity sample. Optimizing the cavity exciton detuning and the detection energy we were able to detect the Kerr angles approaching 90 degrees, which exceeds by one order of magnitude the Kerr rotation angles reported in previous studies. This discovery opens a new perspective for high precision optical measurements of magnetization and spin fluctuations in solids. We develop an original theory showing ways for improving the accuracy of Kerr and Faraday measurements. We believe, this experimental and theoretical work is of general importance as it opens new horizons for optical spin spectroscopy techniques.