The position vectors of the points \(A\), \(B\), \(C\), \(D\) are \(\mathbf{i}+\mathbf{j}+3\mathbf{k}\), \(3\mathbf{i}-\mathbf{j}+5\mathbf{k}\), \(3\mathbf{i}-\mathbf{j}+\mathbf{k}\), and \(5\mathbf{i}-5\mathbf{j}+\alpha\mathbf{k}\), respectively, where \(\alpha\) is a positive integer.

It is given that the shortest distance between the line \(AB\) and the line \(CD\) is equal to \(2\sqrt2\).

(i) Show that the possible values of \(\alpha\) are \(3\) and \(5\).

(ii) Using \(\alpha=3\), find the shortest distance of the point \(D\) from the line \(AC\), giving your answer correct to 3 significant figures.

(iii) Using \(\alpha=3\), find the acute angle between the planes \(ABC\) and \(ABD\), giving your answer correct to 3 significant figures.