Floor , Absolute, Inverse, Sawtooth And Periodic Also

Geometry Level 5

Let \(f(x) = \sin^{-1} (m^2-3m+1) \sec \left( \dfrac{|x|}3 \right) - \lfloor e^{m-4} \rfloor (\sin \{ x \} ) \).

If \(f(x) \) is periodic, find the number of possible non-negative integral value(s) of \(m\).

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