Properties Of Triangle

In the figure, \(\theta_{1}+\theta_{2}=\frac{\pi}{2}\) and \(\sqrt{3}(\mathrm{BE})=4(\mathrm{AB})\). If the area of \(\triangle \mathrm{CAB}\) is \(2 \sqrt{3}-3\) unit \({ }^{2}\), when \(\frac{\theta_{2}}{\theta_{1}}\) is the largest, then the perimeter (in unit) of \(\triangle \mathrm{CED}\) is equal to _________.