When does this area within a circle have a maximum value?

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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

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