In the optical parity-time-symmetry systems, at certain values of their parameters, a phase transition from real eigenvalues of the Hamiltonian to the complex ones is observed. This phase transition, which can be directly or indirectly caused by a change in the measured physical quantity, leads to a sharp change in the optical properties of the system. This can be used to improve the accuracy of various optical sensors, in particular, angular rate sensors. Present communication is devoted to the analysis of previously announced and newly developed by the authors methods for measuring angular rates based on the use of the optical parity-time-symmetry systems. In particular, various variations of laser gyroscopes based on the systems of two identical coupled ring resonators that differ from each other only in the level of losses and gain are considered. We propose a new method for measuring the angular rate, based on the use of a parity-time-symmetry system of two straight coupled waveguides with a passive ring resonator connected to it.