A gardener is trying to fence a garden. The interior of the quadrilateral \(ABCD\) represents her garden where \(AB\) and \(BC\) are walls that are perpendicular to each other. The two fences are such that \(AD = 8\) m, \(DC = 6\) m and \(\angle BAD = \angle DCB = \theta\), where \(\theta\) is an acute angle that varies.
Show that the area of the garden, \(A\) m\(^2\), is given by \(A = 25 \sin 2\theta - 24 \cos 2\theta + 24\).
Express \(A\) in the form of \(R \sin (2\theta - \alpha) + 24\), where \(R > 0\) and \(0^\circ < \alpha < 90^\circ\).
If the gardener wants to fence up an area of \(40\) m\(^2\), find the value of \(\theta\).
With the above dimensions, can the gardener mark out an area of \(60\) m\(^2\)? Justify your answer with clear workings.