Simon congrats on your 100th post mate, your cooking lol.

rotate without using the rotate tool?? now there's an interesting question, that will have me up at night trying to figure that one.

surely as Simon suggests you mean, pan, dolly, zoom via the alt and mouse keys??

should tell you that on the start up tutorial the first and everytime you open Maya until you tick the box that makes it go away, really it is worth a look.

other than that you can rotate the object via the attributes editor, you can hold the contol key down, put the mouse where the red arrow pionts to and press the middle mouse button and drag, the object will rortate, or jusr type it in numerically.

other than that, 'rotating the rotate tool' i think you are having a joke, the rotate tool is meant to rotate the object, not the other way round??