With two joined trapezoidal prisms, calculate the local roll angle of one, when rotation is applied to another

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Given two connected trapezoidal prisms are connected as follows: enter image description here

I can apply a rotation to the prism on the left by rotating about the local X-Axis (top of the prism) - As they are connected the prism on the right will be affected:

enter image description here

My question is: If I do not refer to the first prism, how would I calculate the applied transforms to the second prism in isolation?

I know: a) The rotation angle about the X-Axis applied to the first prism b) The local rotation about the Z-axis of the second prism to make the two prisms join

I would like to calculate the rotation about X & Y axis on the second prism.