  We study the dynamics of optically-induced nuclear spin polarization in a
fluorine-doped ZnSe epilayer via time-resolved Kerr rotation. The nuclear
polarization in the vicinity of a fluorine donor is induced by interaction with
coherently precessing electron spins in a magnetic field applied in the Voigt
geometry. It is detected by nuclei-induced changes in the electron spin
coherence signal. This all-optical technique allows us to measure the
longitudinal spin relaxation time $T_{1}$ of the $^{77}\text{Se}$ isotope in a
magnetic field range from 10 to 130~mT under illumination. We combine the
optical technique with radio frequency methods to address the coherent spin
dynamics of the nuclei and measure Rabi oscillations, Ramsey fringes and the
nuclear spin echo. The inhomogeneous spin dephasing time $T_{2}^{*}$ and the
spin coherence time $T_{2}$ of the $^{77}\text{Se}$ isotope are measured. While
the $T_{1}$ time is on the order of several milliseconds, the $T_{2}$ time is
several hundred microseconds. The experimentally determined condition $T_{1}\gg
T_{2}$ verifies the validity of the classical model of nuclear spin cooling for
describing the optically-induced nuclear spin polarization.
