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

since `p, q gt 0`, we have `pq gt 0`
`tan^(-1) (p -q)/(1 + pq) = tan^(-1) p - tan^(-1) q`....(i)
Since `qr gt -1`, we have
`tan^(-1) (q -r)/(1 + qr) = tan^(-1) q - tan^(-1) r`...(ii)
Since `pr lt -1 and r lt 0`, we have
`tan^(-1) (r - p)/(1 + rp) = pi + tan^(-1) t - tan^(-1) p`....(iii)
On adding Eqs. (i), (ii), and (iii), we get
`tan^(-1) (p -q)/(1 + pq) + tan^(-1) (q - r)/(1 + qr) + tan^(-1) (r - p)/(1 + rp) = pi`