  We calculate Nielsen's circuit complexity of coherent spin state operators.
An expression for the complexity is obtained by using the small angle
approximation of the Euler angle parametrisation of a general $SO(3)$ rotation.
This is then extended to arbitrary times for systems whose time evolutions are
generated by couplings to an external field, as well as non-linearly
interacting Hamiltonians. In particular, we show how the Nielsen complexity
relates to squeezing parameters of the one-axis twisted Hamiltonians in a
transverse field, thus indicating its relation with pairwise entanglement. We
further point out the difficulty with this approach for the
Lipkin-Meshkov-Glick model, and resolve the problem by computing the complexity
in the Tait-Bryan parametrisation.
