Conservation of Angular Momentum (Problem 55)

A diver off the high board imparts an initial rotation with their body fully extended before going into a tuck and executing three back somersaults before hitting the water. If their moment of inertia before the tuck is $16.9\text{kg}\cdot {\text{m}}^2$ and after the tuck during the somersaults is $4.2\text{kg}\cdot {\text{m}}^2$, what rotation rate must the diver impart to their body directly off the board and before the tuck if they take 1.4 s to execute the somersaults before hitting the water?