The complex number u is defined by

\(u = \frac{4i}{1 - (\sqrt{3})i}\).

1. Express u in the form x + iy, where x and y are real and exact.
2. Find the exact modulus and argument of u.
3. On a sketch of an Argand diagram, shade the region whose points represent complex numbers z satisfying the inequalities \(|z| < 2\) and \(|z - u| < |z|\).