Answer
$-\frac{12\sqrt {10}}{31}$
Work Step by Step
Step 1. Let $u=cos^{-1}\frac{3}{7}$, we have $cos(u)=\frac{3}{7}$ and $sin(u)=\sqrt {1-cos^2u}=\frac{2\sqrt {10}}{7}, tan(u)=sin(u)/cos(u)=\frac{2\sqrt {10}}{3}$
Step 2. Use the Double-Angle Formula
$tan(2cos^{-1}\frac{3}{7})=tan(2u)=\frac{2tan(u)}{1-tan^2u}=\frac{4\sqrt {10}}{3(1-40/9)}=-\frac{12\sqrt {10}}{31}$
