How do I rotate the viewport around the local (to the view port) - Z axis?
Basically what you would get if you were to hit R with the camera selected in camera view.
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You can press ⎈ Ctrl⇧ Shift ScrollWheel, or ⇧ ShiftNumpad 4 and ⇧ ShiftNumpad 6.
Currently the scrollwheel binding doesn't exist in 2.8, however you can add it back yourself. Under User Preferences > Input > 3D View > 3D View (Global), press Add New and set the operator to
view3d.view_roll. Create a binding for both left and right:
One non optimal method is to bring the camera to the viewport(Ctrl-Alt-Numberpad 0), select the camera and hit R. This isn't the neatest method, but it still works. It also offers to the degree precision. once positioned, you can delete the camera if it bugs you. see this question on how to "un-roll" the viewport once you're done.