Find value of tan^-1⁡(\(\frac{1}{3}\))+tan^-1⁡(\(\frac{1}{5}\))+tan^-1⁡(\frac{1}{7})[/latex]

Using the formula tan^-1?x+tan^-1?y=tan^-1?\(\frac{x+y}{1-xy}\), we get
tan^-1?(\(\frac{1}{3}\))+tan^-1?(\(\frac{1}{5}\))=tan^-1?\(\bigg(\frac{\frac{1}{3}+\frac{1}{5}}{1-\frac{1}{3}�\frac{1}{5}}\bigg)\)
= \(tan^{-1}\bigg(\frac{\frac{8}{15}}{\frac{14}{15}}\bigg)=tan^{-1}?(\frac{8}{15}�\frac{15}{14})=tan^{-1}?(\frac{4}{7})\)
=\(tan^{-1}(\frac{1}{3})+tan^{-1}(\frac{1}{5})+tan^{-1}?(\frac{1}{7})=tan^{-1}(\frac{4}{7})+tan^{-1}?(\frac{1}{7})\)
=\(tan^{-1}?\bigg(\frac{\frac{4}{7} + \frac{1}{7}}{1-\frac{4}{7}�\frac{1}{7}}\bigg) = tan^{-1}?\bigg(\frac{\frac{5}{7}}{\frac{45}{49}}\bigg)=tan^{-1}?(\frac{5}{7}�\frac{49}{45})\)
=tan^-1?\((\frac{7}{9})\).