  Stellar rotation affects the transport of chemical elements and angular
momentum and is therefore a key process during stellar evolution, which is
still not fully understood. This is especially true for massive stars, which
are important for the chemical enrichment of the universe. It is therefore
important to constrain their physical parameters and internal angular momentum
distribution to calibrate stellar structure and evolution models. Stellar
internal rotation can be probed through asteroseismic studies of rotationally
split oscillations but such results are still quite rare, especially for stars
more massive than the Sun. The SPB star HD201433 is known to be part of a
single-lined spectroscopic triple system, with two low-mass companions orbiting
with periods of about 3.3 and 154 d. Our results are based on photometric
observations made by BRITE - Constellation and the SMEI on board the Coriolis
satellite, high-resolution spectroscopy, and more than 96 years of radial
velocity measurements. We identify a sequence of 9 rotationally split dipole
modes in the photometric time series and establish that HD201433 is in
principle a solid-body rotator with a very slow rotation period of 297+/-76 d.
Tidal interaction with the inner companion has, however, significantly
accelerated the spin of the surface layers by a factor of approximately one
hundred. The angular momentum transfer onto the surface of HD201433 is also
reflected by the statistically significant decrease of the orbital period of
about 0.9 s during the last 96 years. Combining the asteroseismic inferences
with the spectroscopic measurements and the orbital analysis of the inner
binary system, we conclude that tidal interactions between the central SPB star
and its inner companion have almost circularised the orbit but not yet aligned
all spins of the system and have just begun to synchronise rotation.
