  We present the obliquity measurement, that is, the angle between the normal
angle of the orbital plane and the stellar spin axis, of the sub-Neptune planet
HD3167 c, which transits a bright nearby K0 star. We study the orbital
architecture of this multi-planet system to understand its dynamical history.
We also place constraints on the obliquity of planet d based on the geometry of
the planetary system and the dynamical study of the system. New observations
obtained with HARPS-N at the Telescopio Nazionale Galileo (TNG) were employed
for our analysis. The sky-projected obliquity was measured using three
different methods: the Rossiter-McLaughlin anomaly, Doppler tomography, and
reloaded Rossiter-McLaughlin techniques. We performed the stability analysis of
the system and investigated the dynamical interactions between the planets and
the star. HD3167 c is found to be nearly polar with sky-projected obliquity,
$\lambda$ = -97$^{\circ} \pm$ 23$^{\circ}$. This misalignment of the orbit of
planet c with the spin axis of the host star is detected with 97\% confidence.
The analysis of the dynamics of this system yields coplanar orbits of planets c
and d. It also shows that it is unlikely that the currently observed system can
generate this high obliquity for planets c and d by itself. However, the polar
orbits of planets c and d could be explained by the presence of an outer
companion in the system. Follow-up observations of the system are required to
confirm such a long-period companion.
