THz communication has the potential to realize an order of magnitude increase in data rates due to the availability of wide THz-scale spectral bands. Unfortunately, establishing and managing highly directional beams in THz networks is challenging as links lack the "pseudo-omni" reception capability of lower bands and the product of AP-client beam resolution is high due to narrow beams of only a few degrees. In this paper, we present One-shot Path discovEry with a THz RAinbow (OPERA), a novel system that identifies dominant paths between the AP and all clients in order to efficiently steer directional beams. The key idea is to embed path direction into the inherent characteristics of signals traveling along each path. To do so, we exploit a single leaky wave antenna and create a THz Rainbow. A THz Rainbow transmission consists of distinct signals with unique spectral characteristics across the angular domain. Leveraging the spatial-spectral signatures in the THz Rainbow, all receivers can correlate the measured signal with the known transmission signatures to discover the sender's path directions in one-shot. Our experiments demonstrate that OPERA achieves average direction estimates within 2° of ground truth for LOS and reflected paths.