Consider \( f(x)=|x-1|+|2 x-\pi|+|x-3| \) and \( g(x)=\sin ^{-1} x+\tan ^{-1} x \). The value of...

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Consider \( f(x)=|x-1|+|2 x-\pi|+|x-3| \) and \( g(x)=\sin ^{-1} x+\tan ^{-1} x \). The value of \( x \) for which \( f(g(x)) \) is minimum is \( \sqrt{k \sin \frac{\pi}{\lambda}} \) where \( k, \lambda \in N \) then find \( k+\lambda \).
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