\[ \begin{cases} { \sin(x) \cos(y) = \dfrac{1}{4} } \\ { 3 \tan(x) = 4 \tan(y)} \end{cases} \]

If \(x,y\) satisfy the system of equations above, what is the value of \( \lfloor 10000\sin(x+y) \rfloor \)?

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