(a) Showing your working, find the two square roots of the complex number \(1 - (2\sqrt{6})i\). Give your answers in the form \(x + iy\), where \(x\) and \(y\) are exact.

(b) On a sketch of an Argand diagram, shade the region whose points represent the complex numbers \(z\) which satisfy the inequality \(|z - 3i| \leq 2\). Find the greatest value of \(\arg z\) for points in this region.