At what angle θ to the horizontal should an object is projected so...

Given, $H = R$

or $\dfrac{u^{2}\sin^{2}\theta}{2g} = \dfrac{u^{2}\sin 2\theta}{g}$

$\dfrac{\sin \left(\theta\right) \timessin \left(\theta\right)}{2} = 2\sin \left(\theta\right) \timescos \left(\theta\right)$

$⇒ tan\theta =4$

$⇒ \theta = \tan^{-1} \left(4\right)$