The points A, B, C have position vectors \(\mathbf{i} - 2\mathbf{k}, \mathbf{i} + 2\mathbf{j} + 2\mathbf{k}, 2\mathbf{i} - \mathbf{j} - \mathbf{k}\), respectively.

(a) Find the equation of the plane ABC, giving your answer in the form \(ax + by + cz = d\).

A point D has position vector \(\mathbf{i} + t\mathbf{k}\), where \(t \neq -2\).

(b) Find the acute angle between the planes ABC and ABD.

(c) Find the values of \(t\) such that the shortest distance between the lines AB and CD is \(\sqrt{2}\).