Taylor, Maclaurin, & Power series challenge

Find the exact value of the sum of the infinite series given below. $\displaystyle2 -\frac{{{2\pi }^{2}}}{2!}+\frac{{2{\pi }^{4}}}{4!}-...+{{2\left( -1 \right)}^{n}}\frac{{{\pi }^{2n}}}{\left( 2n \right)!}+...$ [[☃ input-number 1]]