If two chords \(PQ\) and \(PR\) on a circle of radius \(1\) meet in an angle \(\theta\) at \(P\), for example as drawn in the diagram below,

then the largest possible area of the shaded region \(RPQ\) is

- \(\theta(1 + \cos\dfrac{\theta}{2})\); \(\quad\)\(\quad\)(b) \(\theta + \sin\theta\); \(\quad\)\(\quad\)(c) \(\dfrac{\pi}{2}(1-\cos\theta)\);\(\quad\)\(\quad\) (d) \(\theta\).