  The inclinations of exoplanets detected via radial velocity method are
essentially unknown. We aim to provide estimations of the ranges of mutual
inclinations that are compatible with the long-term stability of the system.
Focusing on the skeleton of an extrasolar system, i.e., considering only the
two most massive planets, we study the Hamiltonian of the three-body problem
after the reduction of the angular momentum. Such a Hamiltonian is expanded
both in Poincar\'e canonical variables and in the small parameter $D_2$, which
represents the normalised Angular Momentum Deficit. The value of the mutual
inclination is deduced from $D_2$ and, thanks to the use of interval
arithmetic, we are able to consider open sets of initial conditions instead of
single values. Looking at the convergence radius of the Kolmogorov normal form,
we develop a reverse KAM approach in order to estimate the ranges of mutual
inclinations that are compatible with the long-term stability in a KAM sense.
Our method is successfully applied to the extrasolar systems HD 141399, HD
143761 and HD 40307.
