Encouraged by the latest SNO results, we consider the lepton mixing matrix in the approximation that the ν2 mass eigenstate is trimaximally (democratically) mixed. This suggests a new parameterization of the remaining mixing degrees of freedom, which eschews mixing angles, dealing instead, directly with the complex parameter Ue3 of the mixing matrix. Unitarity triangles then take a particularly simple form, which we hope will faciltate comparison with experiment.Recent years have seen huge advances in our knowledge of the properties of neutrinos. Most recently, SNO [1,2] has provided the best evidence for neutrino flavour change, which, coupled with evidence from atmospheric neutrinos [3,4], reactors [5][6][7] and accelerator experiments [8], has enabled the basic form of the MNS [9] lepton mixing matrix, U , to be determined [10].Atmospheric neutrino data [3,4], together with K2K [8] and reactor data [5,6], give (at 68% CL)[10]:Therefore |U τ 3 | 2 ≈ 0.50 ± 0.11, implying thatWe may choose the phases of ν µ and ν τ such that to a good approximationUnitarity then implies that, with the above choice of phases,ie. approximate µ-τ symmetry [11][12][13]. From the analysis of solar neutrino data [14][15][16][17][18], especially from SNO [1, 2], we have (at 68% CL):The phases of ν 2 and ν e can be chosen such thatUnitarity now fixes the remaining three MNS matrix elements up to their overall phase, which may be chosen so thatBoth the relative precision, and the absolute precision, in the determination of |U e2 | 2 in Eq. (5) is better than that of |U µ3 | 2 in Eq. (1), making |U e2 | ≈ 1 √ 3 currently the best-determined of the MNS matrix elements.Equations (3), (7) and (8) together define the tribimaximal mixing texture [19][20][21], which we may take to be the leading approximation to the lepton mixing matrix. This texture is clearly evocative of symmetries at work. Taking the neutrino flavour eigenstates to define the orientation of a cube, the ν 2 eigenstate, Eq. (7), lies along the body diagonal of the cube, while the ν 3 mass eigenstate lies in the plane of the ν µ − ν τ face, at 45 • to the ν µ state. It may be remarked that the same mixing matrix elements also occur as the M = 0 subset of the j × j = 1 × 1 set of Clebsch-Gordan coefficients.An extensive future experimental neutrino program is being planned [22][23][24] which will refine the tribimaximal picture outlined above. The current situation for neutrino physics and the MNS matrix appears analogous to that earlier for B physics and the CKM matrix, in which the leading approximation to the matrix was established experimentally, long before its smallest elements were determined. In that case, the Wolfenstein parametrization has become widely adopted [25]. This approximate paramterization avoids the introduction of mixing angles, dealing instead directly with the complex elements of the matrix, with the help of "unitarity triangles" [26][27][28][29][30][31][32][33]. It is our purpose here to propose an analogously simple parameterization for the MNS mixing...