**Evaluate the Maclaurin series.**
$\dfrac{\pi}{2} -\dfrac{\dfrac{1}{8}{{\pi }^{3}}}{3!}+\dfrac{{\dfrac{1}{32}{\pi }^{5}}}{5!}-...+{{\left( -1 \right)}^{n}}\dfrac{\left(\dfrac{1}{2}\right)^{2n+1}{{\pi }^{2n+1}}}{\left( 2n+1 \right)!}+...$
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