  We present an experimental study of macroscopic and microscopic magnetic
anisotropy of a spin tetramer system \cso using torque magnetometry and ESR
spectroscopy. Large rotation of macroscopic magnetic axes with temperature
observed from torque magnetometry agrees reasonably well with the rotation of
the $\mathbf{g}$ tensor above $T \gtrsim 50$~K. Below 50~K, the $\mathbf{g}$
tensor is temperature independent, while macroscopic magnetic axes continue to
rotate. Additionally, the susceptibility anisotropy has a temperature
dependence which cannot be reconciled with the isotropic Heisenberg model of
interactions between spins. ESR linewidth analysis shows that anisotropic
exchange interaction must be present in \csos. These findings strongly support
the presence of anisotropic exchange interactions in the Hamiltonian of the
studied system. Below $T_N=8$~K, the system enters a long - range
antiferromagnetically ordered state with easy axis along the $<\bar{1} 0 1>^*$
direction. Small but significant rotation of magnetic axes is also observed in
the antiferromagnetically ordered state suggesting strong spin-lattice coupling
in this system.
