There is a relation between the lift to drag ratio (L/D ratio) and the elevation angle, the L/D ratio being the tangent of the elevation angle:
The ground tether angle is obtained by adding the drag of the turbine (roughly its swept area x air density x 0.5, if it is optimized, drag coefficient being roughly 1 or a little less) to the drag of the kite (the drag coefficient is approximately 0.3 or 0.4); then calculating the lift of the kite (the lift coefficient is approximately 1); then lift to drag ratio; then going to Tan(elevation angle).
The same for kiteline angle by removing turbine drag. A good lifter kite has a L/D ratio of 2.4, so an angle of elevation of 67°.
This is an affair of tangent, not cosine. I just corrected an old comment that was not based of the lift to drag ratio (L/D ratio) as tangent.
Hoping this is correct.