If `pgtqgt0` and `prlt-1ltqr`, then find the value of `tan^(-1)((p-q)/(1+pq))+tan^(-1)((q-r)/(1+qr))+tan^(-1)((r-p)/(1+rp))`

Explanation

As `p gt 0, q gt 0 => pq gt 0`

`:. tan^-1((p-q)/(1+pq)) = tan^-1p-tan^-1q->(1)`

As ` qr gt -1`

`:. tan^-1((q-r)/(1+qr)) = tan^-1q-tan^-1r->(2)`

As ` pr lt -1`

`:. tan^-1((r-p)/(1+rp)) = pi +tan^-1r-tan^-1p->(3)`

Adding (1),(2) and (3),

`tan^-1((p-q)/(1+pq))+tan^-1((q-r)/(1+qr)) tan^-1((r-p)/(1+rp)) = tan^-1p-tan^-1q+ tan^-1q-tan^-1r + pi +tan^-1r-tan^-1p`

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