The equation of a curve is \(y = e^{-2x} \tan x\), for \(0 \leq x < \frac{1}{2} \pi\).

(i) Obtain an expression for \(\frac{dy}{dx}\) and show that it can be written in the form \(e^{-2x}(a + b \tan x)^2\), where \(a\) and \(b\) are constants.

(ii) Explain why the gradient of the curve is never negative.

(iii) Find the value of \(x\) for which the gradient is least.