\(A, B, C, D\) are the corners of a square of side \(a\) on level ground. Inside the square is a flagstaff, and the angles of elevation of the top of the flagstaff, as seen from \(A, B, C\) are \(\alpha, \beta, \gamma\) respectively. Find an equation giving the height of the flagstaff in terms of \(\alpha, \beta, \gamma, a\), and deduce that there are two possible values, \(h_1\) and \(h_2\). Show that \[ \frac{1}{h_1^2} + \frac{1}{h_2^2} = \frac{1}{a^2}(\cot^2\alpha+\cot^2\gamma), \] and that \[ 4\cot^2\beta(\cot^2\alpha+\cot^2\gamma-\cot^2\beta) > (\cot^2\alpha-\cot^2\gamma)^2. \]