  Precise characterization of a hyperfine interaction is a prerequisite for
high fidelity manipulations of electron and nuclear spins belonging to a hybrid
qubit register in diamond. Here, we demonstrate a novel scheme for determining
a hyperfine interaction, using single-quantum and zero-quantum Ramsey fringes,
by applying it to the system of a Nitrogen Vacancy (NV) center and a $^{13}$C
nuclear spin in the 1$^{\mathrm{st}}$ shell. The zero-quantum Ramsey fringe,
analogous to the quantum beat in a $\Lambda$-type level structure, particularly
enhances the measurement precision for non-secular hyperfine terms. Precisions
less than 0.5 MHz in the estimation of all the components in the hyperfine
tensor were achieved. Furthermore, for the first time we experimentally
determined the principal axes of the hyperfine interaction in the system.
Beyond the 1$^{\mathrm{st}}$ shell, this method can be universally applied to
other $^{13}$C nuclear spins interacting with the NV center.
