ABSTRACT Θ Mus  = HD 113904 is a massive multiple system containing the WC5/6 + O6/7V binary WR48 in a $19.1\, \mathrm{ d}$ circular orbit. Previous attempts to constrain the variable photometric properties of this binary subsystem have been thwarted by the dominating stochastically variable light from a 10-times brighter blue supergiant (BSG), located only 46 mas away. Even now, with extensive optical space-based photometry from one of the BRITE-Constellation satellites, we were unable to beat down the intrinsic stochastic variability from the BSG enough to provide a convincing detection of a low-level atmospheric eclipse of the WC + O system, as often seen in other short-period WR + O systems. We explore the variability of the dominating BSG and find that its behaviour is similar to that of other BSGs, with a forest of low-frequency Fourier peaks likely from stochastic gravity waves reaching the stellar surface. Then, by adopting an orbital inclination from another more reliable source, we obtain a clumping-independent, linear-density-dependent upper limit of the mass-loss rate for the WR component of $(6.5 \pm 0.3) \times 10^{-5}\, \mathrm{ M}_{\odot }\,\mathrm{ yr}^{ -1}$, which is consistent with values of other WC5/6 subtypes. This corresponds to an upper limit of 5.0 ± 0.2 mmag for the depth of the atmospheric eclipse in the WR48 subsystem when observed together with the BSG.