#### Girls Olympic

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Among all pairs of real numbers $(x, y)$ such that $\sin\sin x=\sin\sin y$ with $-10\pi \le x, y \le 10\pi$. Oleg randomly selected a pair $(X, Y)$. Compute the probability that $X = Y$.

Joel selected an acute angle $x$ (strictly between 0 and 90 degrees) and wrote the value of $\sin x$, $\cos x$, and $\tan x$ on three different cards. Then he gave those cards to three students, Malvina, Paulina, and Georgian, one card to each, and asked them to figure out which trigonometric function (sin, cos, tan) produced their cards. Even after sharing the values on their cards with each other, only Malvian was able to surly identify which function produced the value on her card. Compute the sum of all possible values that Joel wrote on Marlvina's card.