The crystalline electric field (CEF) of Ce3+ in trigonal symmetry has recently become of some relevance, for instance, in the search of frustrated magnetic systems. Fortunately, it is one of the CEF cases in which a manageable analytic solution can be obtained. Here, we present this solution for the general case, and use this result to determine the CEF scheme of the new compound CeIr3Ge7 with the help of T-dependent susceptibility and isothermal magnetization measurements. The resulting CEF parameters B02=34.4K, B04=0.82K, and B34=67.3K correspond to an exceptionally large CEF splitting of the first and second excited levels, 374 K and 1398 K, and a large mixing between the ∣∣±52⟩ and the ∣∣∓12⟩ states. This indicates a very strong easy plane anisotropy with an unusually small c-axis moment. Using the same general expressions, we show that the properties of the recently reported system CeCd3As3 can also be described by a similar CEF scheme, providing a much simpler explanation for its magnetic properties than the initial proposal. Moreover, a similar strong easy plane anisotropy has also been reported for the two compounds CeAuSn and CePdAl4Ge2, indicating that the CEF scheme elaborated here for CeIr3Ge7 corresponds to an exemplary case for Ce3+ in trigonal symmetry.