$x = {1 \over 2}\left( {\tan {\pi \over 9} + \tan {{7\pi } \over {18}}} \right)$ and $2y = \tan {\pi \over 9} + \tan {{5\pi } \over {18}}$ If we interpret the angles in degrees (as suggested by the numbers 20, 50, and 70), we have : $x = \frac{1}{2} \left( \tan 20^\circ + \tan 70^\circ \right),$ and $2y = \tan 20^\circ + \tan 50^\circ.$ The expression for $|x - 2y|$ is then : $|x - 2y| = \left|\frac{\tan 20^\circ + \tan 70^\circ}{2} - \left( \tan 20^\circ + \tan 50^\circ \right)\right|.$ $|x - 2y| = \left|\frac{\tan 20^\circ + \tan 70^\circ - 2 \tan 20^\circ - 2 \tan 50^\circ}{2}\right|,$ which simplifies to : $|x - 2y| = \left|\frac{\tan 70^\circ - \tan 20^\circ - 2 \tan 50^\circ}{2}\right|.$ We know, $\begin{aligned} & \tan 70=\frac{\tan 20+\tan 50}{1-\tan 20 \tan 50} \\\\ &\Rightarrow \tan 70-\tan 70 \cdot \tan 20 \tan 50=\tan 20+\tan 50 \\\\ &\Rightarrow \tan 70-\tan 50-\tan 20-\tan 50=0 \\\\ &\Rightarrow \tan 70-\tan 20-2 \tan 50=0 \end{aligned}$ $\therefore$ $|x - 2y| = \left|\frac{\tan 70^\circ - \tan 20^\circ - 2 \tan 50^\circ}{2}\right|$ = $\left| {{0 \over 2}} \right|$ = 0