The lab-frame speed of light propagating along arm A in the aether theory would satisfy
c2 = v'2A + V2 + 2v'A V cos ?,
where V~ is the velocity of the lab relative to the aether and ? is the angle between V~ and ~v' A. Use this to derive the approximate expression for the lab-frame speed
v'A ? c (1 - ß cos ? - ½ ß2 sin2?,
where ß = V/c. You can drop any terms involving ß3 or higher powers of ß.