  We measure the effective opacity ($\tau_{eff}$) of the Intergalactic Medium
(IGM) from the composite spectra of 281 Lyman-Break Galaxies (LBGs) in the
redshift range $2 \lesssim z \lesssim 3$. Our spectra are taken from the COSMOS
Lyman-Alpha Mapping And Tomographic Observations (CLAMATO) survey derived from
the Low Resolution Imaging Spectrometer (LRIS) on the W.M. Keck I telescope. We
generate composite spectra in two redshift intervals and fit them with spectral
energy distribution (SED) models composed of simple stellar populations.
Extrapolating these SED models into the Ly$\alpha$ forest, we measure the
effective Ly$\alpha$ opacity ($\tau_{eff}$) in the $2.02 \leq z \leq 2.44$
range. At $z = 2.22$, we estimate $\tau_{eff} = 0.159 \pm 0.001$ from a
power-law fit to the data. These measurements are consistent with estimates
from quasar analyses at $z<2.5$ indicating that the systematic errors
associated with normalizing quasar continua are not substantial. We provide a
Gaussian Processes model of our results and previous $\tau_{eff}$ measurements
that describes the steep redshift evolution in $\tau_{eff}$ from $z = 1.5 - 4$.
