A robotic arm's horizontal extension $E$ (in cm) is modelled by the function $E(\alpha )=5\cos 2\alpha +14\cos \alpha$, where $\alpha$ is the motor angle in degrees and $0\le \alpha <360^{\circ }$. Determine, to one decimal place, the values of $\alpha$ for which the extension is exactly 3 cm. (Solutions based entirely on graphical or numerical methods are not acceptable.)