... counterclockwise 45 degrees with respect to z axis means that you look along the +z direction from the origin. The plane of the loop then lies along the same direction as $B$ so $\mu$ and $B$ are now perpendicular. Torque is now a maximum. (See diagram below.)
The magnitude of $\mu$ is still the same ($0.016 Am^2$) because the current and area of the loop are the same. $B$ is still the same - its magnitude is $|B|=0.05T$. So the torque is now $\tau=|\mu| |B| \hat{k}=0.016\times 0.05 \hat{k} Nm=0.0008 \hat{k} Nm$.
The given answer is far too big. It should be the same order of magnitude as (a) but a little bigger.
In the diagram, the magnetic field $B$ (red) lies at $45^{\circ}$ to the x and y axes, and the rectangular loop (blue) initially lies in the yz plane in position $L_1$. (The +z direction points into the screen.)
After the $45^{\circ}$ counter-clockwise rotation about the z axis the rectangular loop lies in position $L_2$. The magnetic moment $u_2$ (green) is normal to the plane of the rectangle and is now perpendicular to $B$. In this position the torque on the rectangular loop $u_2 \times B$ is a maximum.
