A homogeneous shaft with a circular cross$-$section $($diameter $\backslash ($ d $\backslash ))$ is clamped at point $\backslash ($ A $\backslash )$ and subjected to two external torques $\backslash ($ M$\_\{0\}\backslash )$ and $\backslash ($ M$\_\{1\}\backslash )$ at points $\backslash ($ B $\backslash )$ and C$.$

a$)$ The external torque $\backslash ($ M$\_\{0\}\backslash )$ is given. Determine $\backslash (\backslash$boldsymbol$\{$M$\}\_\{1\}\backslash )$ so that the angle of twist is zero at the free end $\backslash ($ C $\backslash ).(2$ points$)$

b$)$ Calculate the maximum shear stress and its location in this case. $(2$ points$)$

Using two methods to solve the problems.