  We perform a comprehensive study of the stellar populations in the young
Large Magellanic Cloud cluster NGC 1866, combining the analysis of its
best-studied Cepheids with that of a very accurate colour-magnitude diagram
(CMD) obtained from the most recent Hubble Space Telescope photometry. We use a
Bayesian method based on new PARSEC stellar evolutionary tracks with
overshooting and rotation to obtain ages and initial rotation velocities of
five well-studied Cepheids of the cluster. We find that four of the five
Cepheids belong to an initially slowly rotating young population (of $ 176 \pm
5$ Myr), while the fifth one is significantly older, either $ 288 \pm 20$ Myr
for models with high initial rotational velocity ($\omega_\mathrm{i} \sim
0.9$), or $ 202 \pm 5$ Myr for slowly rotating models. The complementary
analysis of the CMD rules out the latter solution while strongly supporting the
presence of two distinct populations of $\sim$176 Myr and $\sim$288 Myr,
respectively. Moreover, the observed multiple main sequences and the turn-offs
indicate that the younger population is mainly made of slowly rotating stars,
as is the case of the four younger Cepheids, while the older population is made
mainly of initially fast rotating stars, as is the case of the fifth Cepheid.
Our study not only reinforces the notion that some young clusters like NGC 1866
harbor multiple populations, but gives also hints that the first population,
the older, may inherit the angular momentum from the parent cloud while stars
of the second one, the younger, do not.
