Answer
$76.0^{\circ}$
Work Step by Step
We are given that the range and maximum are the same:
$\implies R=Y_{max}$
$\frac{v_{\circ}^2}{g}sin2\theta=\frac{v_{\circ}^2sin^2\theta}{2g}$
This simplifies to:
$\implies 2sin\theta cos\theta=\frac{1}{2}sin^2\theta$
$4cos\theta=sin\theta$
$\implies tan\theta=4$
$\implies \theta=tan^{-1}4$
$\theta=76.0^{\circ}$
