Tricky Logs

Geometry Level 1

[log10(tan(1))]×[log10(tan(2))]×[log10(tan(3))]××[log10(tan(88))]×[log10(tan(89))]= ? \left [ \log_{10} \left ( \tan \left ( 1^\circ \right ) \right ) \right ] \times \left [ \log_{10} \left ( \tan \left ( 2^\circ \right ) \right ) \right ] \times \left [ \log_{10} \left ( \tan \left ( 3^\circ \right ) \right ) \right ] \times \cdot \cdot \cdot \\ \times \left [ \log_{10} \left ( \tan \left ( 88^\circ \right ) \right ) \right ] \times \left [ \log_{10} \left ( \tan \left ( 89^\circ \right ) \right ) \right ] = \ ?

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