$1\mathrm{.}27$ Figure $1\mathrm{.}83$ shows a three$-$stepped shaft fixed at one end and subjected to a torsional moment $T$ at the other end. The length of step $i$ is $l_i$ and its diameter is $D_i,i=1,2,3.$ All the steps are made of the same material with shear modulus $G_i=G,i=1,2,3.$

a$.$ Find the torsional spring constant $($or stiffness$)k_{t_i}$ of step