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Sample Question 24:
Let \(S\) be the set of all points \((x,y)\) in the coordinate plane such that \(0\leq x\leq \frac\pi 2\) and \(0\leq y\leq \frac\pi 2\). What is the area of the subset of \(S\) for which \(\sin^2 x - \sin x\sin y + \sin^2 y\le \frac 34\)?
\(\mathrm{(A)}\ \frac {\pi^2}9 \qquad \mathrm{(B)}\ \frac {\pi^2}8 \qquad \mathrm{(C)}\ \frac {\pi^2}6 \qquad \mathrm{(D)}\ \frac {3\pi^2}{16} \qquad \mathrm{(E)}\ \frac {2\pi^2}9\)