Context. Young multiple stellar systems can host both circumstellar and circumbinary discs composed of gas and dust, and the orientations of circumbinary discs can be sculpted by the orientation and eccentricity of the central binaries. Studying multiple binary systems and their associated discs enables our understanding of the size and distribution of the planetary systems that subsequently form around them. Aims. A deep (~70%) and extended (~150 days) eclipse was seen towards the young multiple stellar system V773 Tau in 2010. We interpret it as being due to the passage of a circumbinary disc around the B components moving in front of the A components. Our aim is to characterise the orientation and structure of the disc, to refine the orbits of the sub-components, and to predict when the next eclipse will occur. Methods. We combined the photometry from several ground-based surveys, constructed a model for the light curve of the eclipse, and used high angular resolution imaging to refine the orbits of the three spatially resolved components of the system: A, B, and C. A frequency analysis of the light curves, including from the TESS satellite, enabled the characterisation of the rotational periods of the Aa and Ab stars. Results. A toy model of the circumbinary disc shows that it extends out to approximately 5 au around the B binary and has an inclination of 73° with respect to the orbital plane of AB, where the lower bound of the radius of the disc is constrained by the geometry of the AB orbit and the upper bound is set by the stability of the disc. We identify several frequencies in the photometric data that we attribute to rotational modulation of the Aa and Ab stellar companions. We produced the first determination of the orbit of the more distant C component around the AB system and limited its inclination to 93°. Conclusions. The high inclination and large diameter of the disc, together with the expected inclination of the disc from theory, suggest that B is an almost equal-mass, moderately eccentric binary. We identify the rotational periods of the Aa and Ab stars and a third frequency in the light curve that we attribute to the orbital period of the stars in the B binary. We predict that the next eclipse will occur around 2037, during which both detailed photometric and spectroscopic monitoring will characterise the disc in greater detail.
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