An infinite magnetic slab of permeability \(\mu\) has a thickness \(d\), and lies on the \(z = 0\) plane. Below the slab \((z < 0)\), the magnetic flux density \(\mathbf{B}_1\) makes an angle \(\theta_1\) with respect to the \(z\)-axis. In terms of the given values \(B_1\), \(\theta_1\), and \(\mu\), determine
(a) \(B_2\), \(B_3\), \(\theta_2\), and \(\theta_3\),
(b) magnetization surface current densities on the \(z = 0\) and \(z = d\) planes.