Points A (2, 9) and B (3, 0) lie on the curve \(y = 9 + 6x - 3x^2\), as shown in the diagram. The tangent at A intersects the x-axis at C. Showing all necessary working,

(i) find the equation of the tangent AC and hence find the x-coordinate of C,

(ii) find the area of the shaded region ABC.