(a) Find the complex number \(z\) satisfying the equation

\(z + \frac{iz}{z^*} - 2 = 0,\)

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 single Argand diagram sketch the loci given by the equations \(|z - 2i| = 2\) and \(\text{Im} \, z = 3\), where \(\text{Im} \, z\) denotes the imaginary part of \(z\).

(ii) In the first quadrant the two loci intersect at the point \(P\). Find the exact argument of the complex number represented by \(P\).