(a) Find the complex number z satisfying the equation \(z^* + 1 = 2iz\), where \(z^*\) denotes the complex conjugate of \(z\). Give your answer in the form \(x + iy\), where \(x\) and \(y\) are real.

(b) (i) On a sketch of an Argand diagram, shade the region whose points represent complex numbers satisfying the inequalities \(|z + 1 - 3i| \leq 1\) and \(\text{Im } z \geq 3\), where \(\text{Im } z\) denotes the imaginary part of \(z\).

(ii) Determine the difference between the greatest and least values of \(\arg z\) for points lying in this region.