Problem $13\mathrm{.}039-$ Sphere swinging in a vertical plane

The sphere at $\backslash ($ A $\backslash )$ is given a downward velocity $\backslash (\backslash$mathbf$\{$v$\}\_\{0\}\backslash )$ of magnitude $\backslash (5\mathrm{.}90\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ and swings in a vertical plane at the end of a rope of length $\backslash ($ l$=2\backslash$mathrm$\{$~m$\}\backslash )$ attached to a support at $\backslash ($ O $\backslash ).$ Determine the angle $\backslash (\backslash$theta $\backslash )$ at which the rope will break, knowing that it can withstand a maximum tension equal to twice the weight of the sphere. $($Round the final answer to three decimal places.$)$