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We use shuffle and stuffle relations to give a simple proof of a reduction formula for length-two multiple polylogarithms evaluated in complex parameters of absolute value 1 in terms of a finite sum of products of lengthone polylogarithms. This result was originally due to Nakamura and recently reproved by Panzer by different methods. This generalises results of Borwein and Girgensohn for alternating Euler sums and for multiple zeta values twisted by fourth roots of unity by the first author.doi:10.33044/revuma.v59n2a05 fatcat:ksvaj5pmbja2rjooedb274ufoy