KöMaL 2012 C1113

$P$ is the point in the interior of a rectangle ABCD for which the tangents of the angles $\angle$ PAB , $\angle$ PBC , $\angle$ PCD and $\angle$ PDA are 1, 2, $\frac 13$ and $\frac 32$, respectively. What is the tangent of the angle enclosed by the diagonals?