Dihedral Angle in an Octahedron Inscribed in a Sphere

As shown in the figure, the octahedron $PABCDQ$ is inscribed in a sphere with center $O$. The vertices $P$ and $Q$ lie on opposite sides of plane $ABCD$, and both $P\text{-}ABCD$ and $Q\text{-}ABCD$ are regular square pyramids (each apex lies directly above the center of the square base $ABCD$). Let $\theta$ be the plane angle of the dihedral angle $P\text{-}AB\text{-}Q$. Find the range of $\tan \theta$.