The almost hermetic coverage of the CMS detector is used to measure the distribution of transverse energy, ({E}{T}), over 13.2 units of pseudorapidity, (\eta ), for (p\text{Pb}) collisions at a center-of-mass energy per nucleon pair of (\sqrt{{s}{{}{\mathrm{NN}}}}=5.02\phantom{\rule{0.16em}{0ex}}\text{TeV}). The huge angular acceptance exploits the fact that the CASTOR calorimeter at (-6.6<\eta <-5.2) is effectively present on both sides of the colliding system because of a switch in the proton-going and lead-going beam directions. This wide acceptance enables the study of correlations between well-separated angular regions and makes the measurement a particularly powerful test of event generators. For minimum bias (p\text{Pb}) collisions the maximum value of (d{E}{T}/d\eta ) is (22\phantom{\rule{0.16em}{0ex}}\text{GeV}), which implies an ({E}{T}) per participant nucleon pair comparable to that of peripheral PbPb collisions at (\sqrt{{s}{{}{\mathrm{NN}}}}=2.76\phantom{\rule{0.16em}{0ex}}\text{TeV}). The increase of (d{E}{T}/d\eta ) with centrality is much stronger for the lead-going side than for the proton-going side. The (\eta ) dependence of (d{E}_{T}/d\eta ) is sensitive to the (\eta ) range in which the centrality variable is defined. Several modern generators are compared to these results but none is able to capture all aspects of the (\eta ) and centrality dependence of the data and the correlations observed between different (\eta ) regions.