We measure the effective opacity ( \tau _ { \mathrm { 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 _ { \mathrm { eff } } ) in the 2.02 \leq z \leq 2.44 range . At z = 2.22 , we estimate \tau _ { \mathrm { 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 _ { \mathrm { eff } } measurements that describes the steep redshift evolution in \tau _ { \mathrm { eff } } from z = 1.5 - 4 .