Suppose θ is an angle such that θ∈(0,2π), sin2θ<0 and cos2θ>0.
(i) State the quadrant(s) in which the angle 2θ must lie.
(ii) Hence determine the quadrant(s) in which θ must lie.
(iii) Give a brief justification for your answers in parts (i) and (ii), referring to the signs of the trigonometric ratios involved.