[E, Palmer]

I am very likely working on a faulty understanding of FOV but wouldn't this be much simpler?

double AngleToHalfScreen = Vertical_FOV/2;
      
        double OffsetFromMiddle = Math.abs(targetY - pixelHeight/2);

        double FractionofOffset = OffsetFromMiddle/(pixelHeight/2);

        FinalAngle =  AngleToHalfScreen+(AngleToHalfScreen*FractionofOffset);

This is way to simple to be right.

Thank you so much for taking the time to explain this.