The right triangle

Geometry Level pending

Let \(S=\{(x,y) : x\in \{0,1,2,3,4\}, y\in \{0,1,2,3,4,5\},\text{ and } (x,y)\ne (0,0)\}\). Let \(T\) be the set of all right triangles whose vertices are in \(S\). For every right triangle \(t=\triangle{ABC}\) with vertices \(A\), \(B\), and \(C\) in counter-clockwise order and right angle at \(A\), let \(f(t)=\tan(\angle{CBA})\). What is \[\prod_{t\in T} f(t)?\]

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