(a) The complex number u is defined by \(u = \frac{3i}{a + 2i}\), where a is real.

1. Express u in the Cartesian form x + iy, where x and y are in terms of a.
2. Find the exact value of a for which \(\arg u^* = \frac{1}{3} \pi\).

(b)

1. On a sketch of an Argand diagram, shade the region whose points represent complex numbers z satisfying the inequalities \(|z - 2i| \leq |z - 1 - i|\) and \(|z - 2 - i| < 2\).
2. Calculate the least value of \(\arg z\) for points in this region.