Well it depends on how you measure the rotation. It could be called 225 degree cw rotation, or 135 degree ccw rotation. This is assuming that the coins normally have what we call coin orientation.
How does it happen? Well assuming we are dealing with cylinder body dies, the die is normally locked in place in the press by having a flat area ground on the side of the die and then a set screw tightened against it.
If the flat is ground in the wrong place the die will be rotated from where it should be.
If the setscrew works loose the vibration of the press can cause the die to rotate.
The body of the die can crack (split) parallel to the die face and then the die between the die face and the crack can rotate.
We normally say that it is the reverse that has rotated but it could actually be either die that is out of place. Although it will normally be the lower or anvil die because if the setscrew on the upper die becomes loose enough for the die to rotate, it is also loose enough to fall out of the press.
There are other types of dies and oter ways of locking them into the press but that explanation will hold for most US rotated reverse coins.
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