Apar t from several other important results by Schneider [5], little else was known about the arithmetic nature of these numbers until recently. The basic unsolved problem was whether or not 1, co 1, co2, ql, r/2, 2re i are linearly independent over the field of all algebraic numbers. In two papers [-1, 2], Baker made some progress towards an affirmative answer to this problem by employing a generalization to elliptic functions of the transcendence method which he had used to study linear forms in the logarithms of algebraic numbers. Further progress was made in a recent paper by the author [3], in which it was shown that any nonvanishing linear form in the numbers (1), with arbitrary algebraic coefficients, is transcendental. The aim of the present paper is to study one special case of vanishing linear forms in the numbers (1). We establish the following result.