(a)[4]
Determine the complex number $z$ that satisfies the equation $3z - iz^* = 1 + 5i$, where $z^*$ is the complex conjugate of $z$.
(b)[5]
On an Argand diagram, shade the set of points representing complex numbers $z$ that satisfy both $|z| \le 3$ and $\operatorname{Im} z \ge 2$, where $\operatorname{Im} z$ is the imaginary part of $z$. Calculate the largest value of $\arg z$ for points in this region. Give your answer in radians correct to 2 decimal places.