Incredible Tangential Sum

Geometry Level 4

Amazingly, the value of \(\tan\bigg(\displaystyle\sum_{n=1}^{10} \tan^{-1}(n)\bigg)\) can be written in the form \(\frac{a}{b}\) where \(a\) and \(b\) are coprime integers. What is \(a+b\)?

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