Find the value of the expression $\sin \bigg(2\tan^{-1}{\frac{1}{3}}\bigg)+\cos \big(\tan^{-1}2\sqrt 2\big)$

Question

$\begin{array}{1 1} \frac{15}{14} \\ \frac{-15}{14} \\ \frac{14}{15} \\ \frac{-14}{15} \end{array}$