Calculate new pitch and roll after rotating about the z axis

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I am wanting to know how to find out the new pitch and roll values when rotating around a circle. I have become a little stuck on how to achieve this, but hopefully someone will be able to point me in the right direction.

I currently have a circular plate (Yellow in the Picture) that has a specific pitch, roll and heading applied to it. I can work out the overall tilt (blue dot) by taking the pitch vector and the roll vector, using Pythagoras work out the tilt.

Then using Atan, I can find out the bearing to the blue dot.

I then will turn through a specified angle to reach the red dot.

I am struggling to find out how to find out the tilt on the plate at the red dot and how to split that back into the correct pitch and roll vectors?

Plate Tilt