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 $x$ -axis are circular disks with diameters running from the curve $y = \cot x$ to the curve $y = \csc x$ .

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