Hands-free manipulation of 3D objects has long been a challenge for augmented and virtual reality (AR/VR). While many methods use eye gaze to assist with hand-based manipulations, interfaces cannot yet provide completely gaze-based 6 degree-of-freedom (DoF) manipulations in an efficient manner. To address this problem, we implemented three methods to handle rotations of virtual objects using gaze, including RotBar: a method that maps line-of-sight eye gaze onto per-axis rotations, RotPlane: a method that makes use of orthogonal planes to achieve per-axis angular rotations, and RotBall: a method that combines a traditional arcball with an external ring to handle user-perspective roll manipulations. We validated the efficiency of each method by conducting a user study involving a series of orientation tasks along different axes with each method. Experimental results showed that users could accomplish single-axis orientation tasks with RotBar and RotPlane significantly faster and more accurate than RotBall. On the other hand for multi-axis orientation tasks, RotBall significantly outperformed RotBar and RotPlane in terms of speed and accuracy.