A golfer hits a ball from a point \(O\) on horizontal ground with a velocity of \(35\text{ms}^{-1}\) at an angle of \(\theta\) above the horizontal. The horizontal range of the ball is \(R\) and the time of flight is \(t\) seconds.

\((\text{i})\) Express \(t\) in terms of \(\theta\), and hence show that \(R=125 \sin 2 \theta\).

The golfer hits the ball so that it lands \(110 \text{m}\) from \(O\).

\((\text{ii})\) Calculate the two possible values of \(t\).

**Input the sum of the two values of \(t\), correct to 3 significant figures**

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