Given, $Cot\left( {so{{\sec }^{ - 1}}{5 \over 3} + {{\tan }^{ - 1}}{2 \over 3}} \right)$ $= \cot \left( {{{\tan }^{ - 1}}{3 \over 4} + {{\tan }^{ - 1}}{2 \over 3}} \right)$ $= cot\left( {{{\tan }^{ - 1}}{{{3 \over 4} + {2 \over 3}} \over {1 - {3 \over 4} - {2 \over 3}}}} \right)$ $= \cot \left( {{{\tan }^{ - 1}}\left( {{{17} \over 6}} \right)} \right)$ $= \cot \left( {{{\cot }^{ - 1}}{6 \over {17}}} \right)$ $= {6 \over {17}}$