Differential Equations

Let y = y(x) be the solution of the differential equation \({{dy} \over {dx}} + {{\sqrt 2 y} \over {2{{\cos }^4}x - {{\cos }^2}x}} = x{e^{{{\tan }^{ - 1}}(\sqrt 2 \cot 2x)}},\,0 < x < {\pi \over 2}\) with \(y\left( {{\pi \over 4}} \right) = {{{\pi ^2}} \over {32}}\). If \(y\left( {{\pi \over 3}} \right) = {{{\pi ^2}} \over {18}}{e^{ - {{\tan }^{ - 1}}(\alpha )}}\), then the value of 3\(\alpha\)² is equal to ___________.