Find the Function with the Given Derivative Whose Graph Passes $\mathrm { r } ^ { \prime } ( \theta ) = \csc \theta \cot \theta - 3 , \mathrm { P } \left( \frac { 2 \pi } { 3 } , 0 \right)$

Multiple Choice

Find the function with the given derivative whose graph passes through the point P.
- $\mathrm { r } ^ { \prime } ( \theta ) = \csc \theta \cot \theta - 3 , \mathrm { P } \left( \frac { 2 \pi } { 3 } , 0 \right)$

A) $r ( \theta ) = \csc \theta - 3 \theta + \frac { 6 \pi + 2 \sqrt { 3 } } { 3 }$
B) $r ( \theta ) = - \csc \theta - \frac { t ^ { 9 } } { 3 }$
C) $r ( \theta ) = - \csc \theta - 3 \theta$
D) $r ( \theta ) = - \csc \theta - 3 \theta + \frac { 6 \pi + 2 \sqrt { 3 } } { 3 }$