An algebra problem by MaFiA maNiAc

Algebra Level 4

\[ \large \left( 1 - \dfrac1{2^2} \right)\left( 1 - \dfrac1{3^2} \right)\left( 1 - \dfrac1{4^2} \right)\cdots \left( 1 - \dfrac1{2007^2} \right) = \, ? \]

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