Let L₁ be the line through the points (1, 2, 6) and (2, 4, 8). Let L₂ be the line of intersection of the planes P₁ and P₂, where P₁ is the plane x - y + 2z + 1 = 0 and P₂ is the plane through the points (3, 2, -1), (0, 0, 1), and (1, 2, 1). Calculate the distance between L₁ and L₂.