Trignometry - 4

Geometry Level 2

{sin(x)cos(y)=143tan(x)=4tan(y) \begin{cases} { \sin(x) \cos(y) = \dfrac{1}{4} } \\ { 3 \tan(x) = 4 \tan(y)} \end{cases}

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

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