Techniques of Differentiation - Derivatives of Trigonometric Functions

The diagram shows a trapezium \(OPQR\), where \(OR = 6\) cm and angle \(OPQ = \text{angle}\hspace{0.5em} PQR = \frac{\pi}{2}\) radians. Angle \(ROP = \theta\) radians, where \(\theta\) is acute. \(T\) is a point on \(PQ\) such that angle \(ORT = \frac{\pi}{2}\) radians and \(RT = 3\) cm.

1. Show that the area of the trapezium \(OPQR\), in cm\(^2\), is \(9 \sin 2\theta + 18 \sin^2 \theta\).
2. Given that \(\theta\) can vary, find the exact value of \(\theta\) for which the area of trapezium \(OPQR\) is stationary.
3. Determine whether this value of \(\theta\) gives a maximum or minimum value of the area.