解题---Here is the extracted content from the image: **Problem Statement:** It is given that ellipse E: `x^2/a^2 + y^2/b^2 = 1` (where `a > b > 0`) has a focal length of `2√3`. Line `l: y = kx + 1` passes through point `M(1, 1/2)`, and intersects ellipse E at points P and Q. M is the midpoint of line segment PQ, and O is the origin. **(1) Find the equation of ellipse E.** **(2) If the vertices of trapezoid ABCD are all on ellipse E, and AB is parallel to CD, diagonals AC and BD intersect at point M, and the midpoints of line segments AB and CD are G and H respectively.** **(i) Prove that points G, H, O, M are collinear.** **(ii) Investigate whether the intersection point of line AD and line BC is a fixed point. If it is, find the fixed point and prove it; if not, explain why.**