Rate coefficients, k, for the gas-phase reaction of the OH radical with (E)- CF3CH=CHCF3 ((E)-l,l,l,4,4,4-hexafluoro-2-butene, HFO-1336mzz(E)) were measured over a range of temperatures (211-374 K) and bath gas pressures (20-300 Torr; He, N-2) using a pulsed laser photolysis-laser-induced fluorescence (PLP-LIF) technique. k(1)(T) was independent of pressure over this range of conditions with k(1)(296 K) = (1.31 +/- 0.15) X 10(-13) cm(3) molecule(-1) s(-1) and fcj(T) = (6.94 +/- 0.80) X 10(-13)exp[-(496 +/- 10)/T] cm(3) molecule(-1) s(-1), where the uncertainties are 2 sigma, and the pre-exponential term includes estimated systematic error. Rate coefficients for the OD reaction were also determined over a range of temperatures (262-374 K) at 100 Torr (He). The OD rate coefficients were similar to 15% greater than the OH values and showed similar temperature dependent behavior with k(2)(T) = (7.52 +/- 0.44) X 10(-13)exp[-(476 +/- 20)/T] and k(2)(296 K) = (1.53 +/- 0.15) X 10(-13) cm(3) molecule(-1) s(-1). The rate coefficients for reaction 1 were also measured using a relative rate technique between 296 and 375 K with k(1),(296 K) measured to be (1.22 +/- 0.l) X 10(-13) cm(3) molecule(-1) s(-1), in agreement with the PLP-LIF results. In addition, the 296 K rate coefficient for the O-3 + (E)CF3CH=CHCF3 reaction was determined to be <5.2 X 10(-22) cm(3) molecule(-1) s(-1). A theoretical computational analysis is presented to interpret the observed positive temperature dependence for the addition reaction and the significant decrease in OH reactivity compared to the (Z)-CF3CH=CHCF3 stereoisomer reaction. The estimated atmospheric lifetime of (E)-CF3CH= CHCF3, due to loss by reaction with OH, is estimated to be similar to 90 days, while the actual lifetime will depend on the location and season of its emission. Infrared absorption spectra of (E)-CF3CH=CHCF3 were measured and used to estimate the 100 year time horizon global warming potentials (GWP) of 32 (atmospherically well-mixed) and 14 (lifetime-adjusted).