ControlRotation that points Pawn's weapon at target

Development Character & Animation
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I have a Pawn which I am controlling using a PlayerController.
The Pawn has a child weapon attached to it.
The weapon has a socket attached to it that defines the direction that bullets fly.
The weapon is offset both by position (Vector) and possibly rotation (Rotator/Quaternion) in 3 dimensions (X, Y, Z).

How do I calculate a Control Rotation for the Pawn, which by rotating the pawn, points the weapon’s forward vector at the target? (used with SetControlRotation, in the PlayerController).

325462-setcontrolrotation.png

Pointing the Pawn at the target is easy with a LookAt rotation. It is the weapon offset in 3D that gives me trouble.
I would like the calculations before rotating the Pawn; I want to avoid any solution that first turns the Pawn and then turns it again to correct the offset. One turn only, please.

Thanks in advance for any help!