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Westerlund 1 (Wd 1) is one of the most massive young star clusters in the Milky Way. Although relevant for star formation and evolution, its fundamental parameters are not yet very well constrained. We aim to derive an accurate distance and provide constraints on the cluster age. We used the photometric and astrometric information available in the Gaia Early Data Release 3 (Gaia-EDR3) to infer its distance of 4.06$^{+0.36}_{-0.34}$ kpc. Modelling of the eclipsing binary system W36, reported in Paper II, led to the distance of 4.03 ± 0.25 kpc, in agreement with the Gaia-EDR3 distance and, therefore, validating the parallax zero-point correction approach appropriate for red objects. The weighted average distance based on these two methods results in dwd1  =  4.05 ± 0.20 kpc (m − M  =  13.04$^{+0.11}_{-0.12}$ mag), which has an unprecedented accuracy of 5 per cent. Using the Binary Population and Spectral Synthesis (BPASS) models for the Red Supergiants with solar abundance, we derived an age of 10.7 ± 1 Myr, in excellent agreement with recent work by Beasor & Davies (10.4$^{+1.3}_{-1.2}$ Myr) based on MIST evolutionary models. In Paper II, W36B was reported to be younger than 7.1 Myr, supporting recent claims of a temporal spread of several Myrs for the star-forming process within Wd 1 instead of a single monolithic starburst episode scenario.

Westerlund 1 (Wd 1) is one of the most relevant star clusters in the Milky Way to study massive star formation, although it is still poorly known. Here, we used photometric and spectroscopic data to model the eclipsing binary W36, showing that its spectral type is O6.5 III  +  O9.5 IV, hotter and more luminous than thought before. Its distance dW36 = 4.03 ± 0.25 kpc agrees, within the errors, with three recent Gaia-EDR3-based distances reported in Paper I, Beasor & Davies, and by Negueruela’s group. However, they follow different approaches to fix the zero-points for red sources such as those in Wd 1, and to select the best approach, we used an accurate modelling of W36. The weighted mean distance of our parallax (Paper I) and binary distances results in dwd1 = 4.05 ± 0.20 kpc, with an unprecedented accuracy of 5 per cent. We adopted isochrones based on the Geneva code with supersolar abundances to infer the age of W36B as 6.4 ± 0.7 Myr. This object seems to be part of the prolific star formation burst represented by OB giants and supergiants that occurred at 7.1 ± 0.5 Myr ago, which coincides with the recently published PMS isochrone with age 7.2 Myr. Other BA-type luminous evolved stars and yellow hypergiants spread in the age range of 8–11 Myr. The four red supergiants discussed in paper I represent the oldest population of the cluster with an age of 10.7 ± 1 Myr. The multiple episodes of star formation in Wd 1 are reminiscent of that reported for the R136/30 Dor LMC cluster.