Distance and age of the massive stellar cluster Westerlund 1. I.
  Parallax method using Gaia-EDR3
  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. Our goal is 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
4.34$\pm$0.25 kpc, in agreement with the Gaia-EDR3 distance and, therefore,
validating the parallax zero-point correction approach appropriate for red
objects. By taking advantage of another two recent distance determinations
using the Gaia-EDR3, we obtained a weighted mean distance for the cluster as
d$_{\rm wd1}$=4.23$^{+0.15}_{-0.13}$ kpc ($m-M$=13.13$^{+0.08}_{-0.07}$ mag),
which has an unprecedented accuracy of 4\%. We adopted recent Geneva
evolutionary tracks for supra-solar metallicity objects to infer the age of the
faintest RSG source from Wd 1, leading to a cluster age of 11.0$\pm$0.5 Myr, in
excellent agreement with recent work by Beasor \& Davies (10.4$^{+1.3}_{-1.2}$
Myr) based on MIST evolutionary models. The age of W36 was reported to be
3.5$\pm$0.5 Myr in Paper II, supporting recent claims of a temporal spread of
several Myr for the star-forming process within Wd 1 instead of a monolithic
starburst scenario.
