Straight Lines And Pair Of Straight Lines

If the point \(\left(\alpha, \frac{7 \sqrt{3}}{3}\right)\) lies on the curve traced by the mid-points of the line segments of the lines \(x \cos \theta+y \sin \theta=7, \theta \in\left(0, \frac{\pi}{2}\right)\) between the co-ordinates axes, then \(\alpha\) is equal to :