(i) Differentiate \((\cos x)^{-1}\) with respect to \(x\).

(ii) Hence find \(\dfrac{dy}{dx}\), given that \(y=\tan x+4(\cos x)^{-1}\).

(iii) Using your answer to part (ii), find the values of \(x\) in the range \(0\leq x\leq2\pi\) such that \(\dfrac{dy}{dx}=4\).