The variables x and y satisfy the differential equation

\(\frac{dy}{dx} = e^{-2y} \tan^2 x\),

for \(0 \leq x < \frac{1}{2}\pi\), and it is given that \(y = 0\) when \(x = 0\). Solve the differential equation and calculate the value of \(y\) when \(x = \frac{1}{4}\pi\).