We propose a sensitive and stable three-axis gyroscope in diamond. We achieve high sensitivity by exploiting the long coherence time of the N14 nuclear spin associated with the Nitrogen-Vacancy center in diamond, and the efficient polarization and measurement of its electronic spin. While the gyroscope is based on a simple Ramsey interferometry scheme, we use coherent control of the quantum sensor to improve its coherence time as well as its robustness against long-time drifts, thus achieving a very robust device with a resolution of 0.5mdeg/s/(Hz mm^3)^(1/2). In addition, we exploit the four axes of delocalization of the Nitrogen-Vacancy center to measure not only the rate of rotation, but also its direction, thus obtaining a compact three-axis gyroscope.