Find the Volume of the Described Solid $x$ -Axis At $x = \pi / 6$

Multiple Choice

Find the volume of the described solid.
-The solid lies between planes perpendicular to the $x$ -axis at $x = \pi / 6$ to $x = \pi / 2$ . The cross sections perpendicular to the $\mathrm { x }$ -axis are circular disks with diameters running from the curve $\mathrm { y } = \cot \mathrm { x }$ to the curve $\mathrm { y } = \csc \mathrm { x }$ .

A) $( 2 \sqrt { 3 } - 2 ) \pi - \frac { \pi ^ { 2 } } { 3 }$
B) $( \sqrt { 3 } - 1 ) \pi + \frac { \pi ^ { 2 } } { 6 }$
C) $\frac { ( \sqrt { 3 } + 1 ) \pi } { 2 } - \frac { \pi ^ { 2 } } { 6 }$
D) $\frac { ( \sqrt { 3 } - 1 ) \pi } { 2 } - \frac { \pi ^ { 2 } } { 12 }$