A rod of length 2 cm makes an angle `(2pi )/(3)` rad with the principal axis of a thin convex lens. The lens has a focal length of 10 cm and is placed at a distance of `( 40)/(3) cm ` from the object as shown in the figure . The height of the image is `( 30 sqrt(3))/(13) cm` and the angle made by it with respect to the principal axis is ` alpha ` rad . The value of ` alpha ` is `(pi )/(n)` rad , where n is ____.