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$2 \tan ^{-1}\left(\frac{1}{3}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=$
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$\frac{\pi}{2}$
$\begin{aligned} & 2 \tan ^{-1}\left(\frac{1}{3}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\tan ^{-1} \frac{2 \times \frac{1}{3}}{1-\left(\frac{1}{3}\right)^2}+\cos ^{-1}\left(\frac{3}{5}\right) \\ & =\tan ^{-1}\left(\frac{\frac{2}{3}}{\frac{8}{9}}\right)+\cos ^{-1}\left(\frac{3}{5}\right) \\ & =\tan ^{-1}\left(\frac{3}{4}\right)+\cot ^{-1}\left(\frac{3}{4}\right) \\ & =\frac{\pi}{2}\end{aligned}$
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