Ellipse

When the origin is shifted to the point $(h, k)$ by translating the coordinates axes, the equation $S \equiv 2 x^2-x y+y^2+2 x+3 y+1=0$ is changed to $S \equiv a x^2+2 h x y+b y^2-3=0$. Again by rotating the coordinate axes about the new origin through the angle $\theta$ in the positive direction, $S^{\prime}=0$ is changed to $A x^2+B y^2+C=0$. Then, $h+k+\tan 2 \theta=$