We measure the effective opacity ({tau}_eff_) of the intergalactic medium from the composite spectra of 281 Lyman-break galaxies in the redshift range 2<~z<~3. Our spectra are taken from the COSMOS Ly{alpha} Mapping And Tomographic Observations survey derived from the Low Resolution Imaging Spectrometer 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<~z<~2.44 range. At z=2.22, we estimate {tau}_eff_=0.159{+/-}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.