$\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,\,\,Let\,v\,be\,velocity\,of\,projectile\,at\\
{\rm{maximum}}\,{\rm{height}}\,{\rm{H}}{\rm{.}}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,v\, = \,u\cos \theta \\
According\,to\,given\,problem,\,v = \frac{u}{2}\\
\therefore \,\frac{u}{2} = \,u\cos \,\theta  \Rightarrow \cos \theta \frac{1}{2} \Rightarrow \theta  = {60^ \circ }
\end{array}$