The numbers \(p\) and \(q\) are such that the parabolas \(y = - 2x^2\) and \(y = x^2 + px + q\) intersect at two points, bounding a certain figure.
Find the equation of the vertical line dividing the area of this figure in half.
Calculate \(\int_0^{\pi/2} (\sin^2 (\sin x) + \cos^2 (\cos x))\,dx\).