# Problem #1252

 1252 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 $\sin^2 x - \sin x\sin y + \sin^2 y\le \frac 34$? $\mathrm{(A)}\ \frac {\pi^2}9 \qquad \mathrm{(B)}\ \frac {\pi^2}8 \qquad \mathrm{(C)}\ \frac {\pi^2}6 \qquad \mathrm{(D)}\ \frac {3\pi^2}{16} \qquad \mathrm{(E)}\ \frac {2\pi^2}9$ This problem is copyrighted by the American Mathematics Competitions.
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• Reduce fractions to lowest terms and enter in the form 7/9.
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