Happy new functions 2018!!

For any positive integer $n$ , define $f_n : (0, \infty) \rightarrow \mathbb R$ as

$\large\ { f }_{ n }\left( x \right) = \displaystyle \sum _{ j=1 }^{ n }{ \tan ^{ -1 }{ \left( \frac { 1 }{ 1 + \left( x + j \right) \left( x + j - 1 \right) } \right) } } \forall x \in \left( 0, \infty \right)$ .

Find the value of

$\large\ \sum _{ j=1 }^{ 5 }{ \tan ^{ 2 }{ \left( { f }_{ j }\left( 0 \right) \right) } }$ .