  We analyze the contributions of Nambu-Goldstone modes to the shear viscosity
of a superfluid atomic Fermi gas close to unitarity. We show that the low
temperature experimental values of the shear viscosity to entropy ratio,
$\eta/s$, are reproduced considering an effective shear viscosity which takes
into account the collisions among Nambu-Goldstone bosons and the finite size of
the optical trap. We predict that, for $T \lesssim 0.1 T_F$, $\eta/s$ should
correlate with the size of the trap and linearly decrease with decreasing
temperature. For $T \gtrsim 0.1 T_F$, we find agreement with the experimental
data assuming that the Nambu-Goldstone modes have an anomalous dispersion law.
