Solve the equation tan2θ=3tanθ for 0<θ<2π and answer the following:
(i) Express the given equation as a quadratic equation in tanθ, clearly stating any restrictions required for its validity.
(ii) Solve the quadratic equation to obtain all possible values of tanθ.
(iii) From the values obtained in part (ii), write the general solution(s) for θ, considering all necessary conditions on θ.
(iv) Hence, list all solutions of the original equation that lie strictly between 0 and 2π. Arrange them in ascending order.