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We consider the problem of joint three-dimensional localization and synchronization for a single-input single-output (SISO) system in the presence of a reconfigurable intelligent surface (RIS), equipped with a uniform planar array. First, we derive the Cramér-Rao bounds (CRBs) on the estimation error of the channel parameters, namely, the angle-of-departure (AOD), composed of azimuth and elevation, from RIS to the user equipment (UE) and times-of-arrival (TOAs) for the path from the base station (BS) to UE and BS-RIS-UE reflection. In order to avoid high-dimensional search over the parameter space, we devise a low-complexity estimation algorithm that performs two 1D searches over the TOAs and one 2D search over the AODs. Simulation results demonstrate that the considered RIS-aided wireless system can provide submeter-level positioning and synchronization accuracy, materializing the positioning capability of Beyond 5G networks even with single-antenna BS and UE. Furthermore, the proposed estimator is shown to attain the CRB at a wide interval of distances between UE and RIS. Finally, we also investigate the scaling of the position error bound with the number of RIS elements.