(i) Without using a calculator, solve the equation \(6c^3-7c^2+1=0\).

It is given that \(y=\tan x+6\sin x\).

(ii) Find \(\dfrac{dy}{dx}\).

(iii) If \(\dfrac{dy}{dx}=7\), show that \(6\cos^3x-7\cos^2x+1=0\).

(iv) Hence solve the equation \(\dfrac{dy}{dx}=7\), for \(0\leq x\leq\pi\) radians.