Definite Integration

Let \(f\) be \(a\) differentiable function defined on \(\left[ {0,{\pi \over 2}} \right]\) such that \(f(x) > 0\) and \(f(x) + \int_0^x {f(t)\sqrt {1 - {{({{\log }_e}f(t))}^2}} dt = e,\forall x \in \left[ {0,{\pi \over 2}} \right]}\). Then \(\left( {6{{\log }_e}f\left( {{\pi \over 6}} \right)} \right)^2\) is equal to __________.