\(ABCD\) is a uniform square lamina of side \(6a\). Points \(E\) and \(F\) are on \(DC\) and \(AB\), respectively, and are such that \(DE=FB=h\). The quadrilateral \(BCEF\) is removed from the square lamina.

(a) Show that the distance of the centre of mass of the resulting lamina \(AFED\) from \(AD\) is \(\dfrac{h^2-6ah+36a^2}{18a}\), and find a corresponding expression for the distance of the centre of mass from \(AB\).

When the lamina \(AFED\) is suspended from the point \(D\), the edge \(DA\) makes an angle \(\theta\) with the downward vertical, where \(\tan\theta=\dfrac{7}{15}\).

(b) Find, in terms of \(a\), the two possible values of \(h\).