# Horse Grazing

Calculus Level 4

A horse is tethered by a rope fastened at one end $$A$$ on the boundary of a circular field whoose center is $$O$$. The horse can graze over $$\dfrac { 1 } { 7 }$$ the part of the field reaching the farthest point $$B$$ on the boundary that he can reach. If $$\angle AOB = \theta$$. Find the value of $\dfrac { 7(\sin { \theta +\left( \pi -\theta \right) \cos { \theta } ) } }{ \pi }.$

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