Suppose that $0 < c < \pi/2.$ For what value of $c$ is the area of the region enclosed by the curves $y=\cos(x),$ $y=\cos(x-c),$ and $x=0$ equal to the area of the region enclosed by the curves $y=\cos(x-c),$ $x=\pi,$ and $y=0$?

$c =$