Checkers, Anyone?

Calculus Level 3

The graph of csc(x)csc(y)=ϕ\csc(x)\csc(y)=\phi forms a bunch of squares and circles. The area of one of these circles is most nearly which of the following?

Remark: ϕ=1+52\phi = \frac{1+\sqrt{5}}{2}

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