We investigate the stellar populations of 25 massive, galaxies ($log[M_ast/M_odot] geq 10.9$) at $1.5 < z < 2$ using data obtained with the K-band Multi-Object Spectrograph (KMOS) on the ESO VLT. Targets were selected to be quiescent based on their broadband colors and redshifts using data from the 3D-HST grism survey. The mean redshift of our sample is $bar{z} = 1.75$, where KMOS YJ-band data probe age- and metallicity-sensitive absorption features in the rest-frame optical, including the $G$ band, Fe I, and high-order Balmer lines. Fitting simple stellar population models to a stack of our KMOS spectra, we derive a mean age of $1.03^{+0.13}_{-0.08}$ Gyr. We confirm previous results suggesting a correlation between color and age for quiescent galaxies, finding mean ages of $1.22^{+0.56}_{-0.19}$ Gyr and $0.85^{+0.08}_{-0.05}$ Gyr for the reddest and bluest galaxies in our sample. Combining our KMOS measurements with those obtained from previous studies at $0.2 < z < 2$ we find evidence for a $2-3$ Gyr spread in the formation epoch of massive galaxies. At $z < 1$ the measured stellar ages are consistent with passive evolution, while at $1 < z lesssim2$ they appear to saturate at $sim$1 Gyr, which likely reflects changing demographics of the (mean) progenitor population. By comparing to star-formation histories inferred for normal star-forming galaxies, we show that the timescales required to form massive galaxies at $z gtrsim 1.5$ are consistent with the enhanced $alpha$-element abundances found in massive local early-type galaxies.
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