The Generalized Degrees of Freedom (GDoF) of the two user interference channel are characterized for all parameter regimes under the assumption of finite precision channel state information at the transmitters (CSIT), when a limited amount of (half-duplex or full-duplex) cooperation is allowed between the transmitters in the form of $π$ DoF of shared messages. In all cases, the number of over-the-air bits that each cooperation bit buys is shown to be equal to either $0, 1, 1/2$ or $1/3$. The most interesting aspect of the result is the $1/3$ slope, which appears only under finite precision CSIT and strong interference, and as such has not been encountered in previous studies that invariably assumed perfect CSIT. Indeed, the achievability and converse for the parameter regimes with $1/3$ slope are the most challenging aspects of this work. In particular, the converse relies on non-trivial applications of Aligned Images bounds.