Consider the vectors x = î + 2ĵ + 3k^, y = 2î + 3ĵ + k^, and z = 3î + ĵ + 2k^. For two distinct positive real numbers α and β, define X = αx + βy − z, Y = αy + βz − x, and Z = αz + βx − y. If the vectors X, Y, and Z lie in a plane, then the value of α + β − 3 is _______________.