The position vectors of the points \(A, B, C, D\) are
\(\mathbf{i}+\mathbf{j}+3 \mathbf{k}, \quad 3 \mathbf{i}+4 \mathbf{j}+5 \mathbf{k}, \quad-\mathbf{i}+3 \mathbf{k}, \quad m \mathbf{j}+4 \mathbf{k},\)
respectively, where \(m\) is a constant.
(i) Show that the lines \(A B\) and \(C D\) are parallel when \(m=\frac{3}{2}\).

(ii) Given that \(m \neq \frac{3}{2}\), find the shortest distance between the lines \(A B\) and \(C D\).

(iii) When \(m=2\), find the acute angle between the planes \(A B C\) and \(A B D\), giving your answer in degrees.