The antiferromagnetically ordered state of the monoclinic quasi-one-dimensional S = 1/2 Heisenberg antiferromagnet CuSb2O6 was studied combining torque magnetometry with a phenomenological approach to magnetic anisotropy. This system is known to have a number of different twins in the monoclinic beta phase, which differ in the orientation of the two CuO6 octahedra in the unit cell resulting in different orientation of magnetic axes with respect to crystal axes for each twin. We performed torque measurements in magnetic fields H <= 0.8 T on a sample where a certain type of twin was shown to be dominant by ESR spectroscopy. The measured data reveal that the easy axis is the crystallographic b axis for this sample. Phenomenological magnetocrystalline anisotropy energy invariant to crystal symmetry operations was used to model the spin axis direction in zero and finite magnetic fields. Our model reproduces the value of the spin-flop field H-SF = 1.25 T found in literature. A combination of this approach with our torque results shows that the spin axis will flop in the direction of the maximal value of measured g tensor when the magnetic fieldH > H-SF is applied along the easy axis direction. Our analysis of magnetocrystalline anisotropy energy predicts two possibilities for the easy axis direction in this system, b or a, connected to different crystallographic twins that can be realized in CuSb2O6. These results offer a possibility to reconcile the different reports of easy axis direction found in literature for this system and also nicely demonstrate how a combination of torque magnetometry and a phenomenological approach to magnetic anisotropy can be used to determine the value of the spin-flop field and the direction of spin axis in antiferromagnets in bothH < H-SF andH > H-SF by performing measurements in fields significantly smaller than H-SF.