Find the value of `4 tan^(-1).(1)/(5) - tan^(-1).(1)/(70) + tan^(-1).(1)/(99)`

Explanation

`4 tan^(-1).(1)/(5) - tan^(-1). (1)/(70) + tan^(-1). (1)/(99)`
`= 2 tan^(-1) [((2)/(5))/(1 - (1)/(25))] - tan^(-1).(1)/(70) + tan^(-1).(1)/(99)`
`= 2 tan^(-1) ((5)/(12)) + tan^(-1) [((1)/(99) - (1)/(70))/(1 + (1)/(99) xx (1)/(70))]`
`= tan^(-1) [((5)/(6))/(1 - (25)/(144))] + tan^(-1) ((-29)/(6931))`
`= tan^(-1) ((120)/(119)) - tan^(-1) ((1)/(239))`
`= tan^(-1) [((120)/(119) - (1)/(239))/(1 + (120)/(119) xx (1)/(239))] = tan^(-1) (1) = (pi)/(4)`