Inverse tan series

Geometry Level 3

tan[tan1(12)+tan1(29)+tan1(18)+tan1(225)+tan1(118)+] \tan \left [ \tan^{-1}\left(\frac12\right)+\tan^{-1}\left(\frac29\right)+\tan^{-1}\left(\frac18\right)+\tan^{-1}\left(\frac2{25}\right)+\tan^{-1}\left(\frac1{18}\right)+\ldots \right]

What is the value of the expression above?

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