**Use the fact that ** $\displaystyle\frac{d}{dx}\left( \arctan (2x) \right)\text{ = }\frac{2}{1+{{(2x)}^{2}}}$ **to find the coefficient of the fourth nonzero term in the power series representation of $~\arctan \left( 2x \right)\,$.** [[☃ math-keypad 1]]