The emergence of chemical complexity during star and planet formation is largely guided by the chemistry of unstable molecules that are reaction intermediates in terrestrial chemistry. Our knowledge of these intermediates is limited by both the lack of laboratory studies and the difficulty in their astronomical detection. In this work, we focus on the weakly bound cluster HO3 as an example of the connection between laboratory spectroscopic study and astronomical observations. Here, we present a fast-sweep spectroscopic technique in the millimeter and submillimeter range to facilitate the laboratory search for trans-HO3 and DO3 transitions in a discharge supersonic jet and report their rotational spectra from 70 to 450 GHz. These new measurements enable full determination of the molecular constants of HO3 and DO3. We also present a preliminary search for trans-HO3 in 32 star-forming regions using this new spectroscopic information. HO3 is not detected, and column density upper limits are reported. This work provides additional benchmark information for computational studies of this intriguing radical, as well as a reliable set of molecular constants for extrapolation of the transition frequencies of HO3 for future astronomical observations.