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The answer is: it's not a rotation. If you visualize the circular rails around which the vertices would travel in a rotation, you can see that.
If you wanted a transform to do the job, on parallel rails, it would be a shear. (ShiftCtrlAltS). But that's expressed in terms of offset, which would be half the length of the vertical edge to get 45 degrees, and would be awkward.
So the best idea here is probably a cut. Hit K and left-click on your starting vertex. It should highlight green. Hit C to snap the cut to 45 degrees, (and Z if you need to cut through more than one layer of faces), and move the mouse over to the opposite edge, until you see the highlight again. Left-click to 'plant' the other end of the cut, and the Space bar to confirm it.