The multi-sector intelligent surface (IS), benefiting from a smarter wave manipulation capability, has been shown to enhance channel gain and offer full-space coverage in communications. However, the benefits of multi-sector IS in wireless sensing remain unexplored. This paper introduces the application of multi-sector IS for wireless sensing/localization. Specifically, we propose a new self-sensing system, where an active source controller uses the multi-sector IS geometry to reflect/scatter the emitted signals towards the entire space, thereby achieving full-space coverage for wireless sensing. Additionally, dedicated sensors are installed aligned with the IS elements at each sector, which collect echo signals from the target and cooperate to sense the target angle. In this context, we develop a maximum likelihood estimator of the target angle for the proposed multi-sector IS self-sensing system, along with the corresponding theoretical limits defined by the Cramér-Rao Bound. The analysis reveals that the advantages of the multi-sector IS self-sensing system stem from two aspects: enhancing the probing power on targets (thereby improving power efficiency) and increasing the rate of target angle (thereby enhancing the transceiver's sensitivity to target angles). Finally, our analysis and simulations confirm that the multi-sector IS self-sensing system, particularly the 4-sector architecture, achieves full-space sensing capability beyond the single-sector IS configuration. Furthermore, similarly to communications, employing directive antenna patterns on each sector's IS elements and sensors significantly enhances sensing capabilities. This enhancement originates from both aspects of improved power efficiency and target angle sensitivity, with the former also being observed in communications while the latter being unique in sensing.