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tan^(-1)""(1)/(5)+tan^(-1)""(1)/(7)+tan^...

`tan^(-1)""(1)/(5)+tan^(-1)""(1)/(7)+tan^(-1)""(1)/(3)+tan^(-1)""(1)/(8)=(pi)/(4)`

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`L.H.S.=tan^(-1)""(1)/(5)+tan^(-1)""(1)/(7)+tan^(-1)""(1)/(3)+tan^(-1)""(1)/(8)`
`=tan^(-1)""((1)/(5)+(1)/(7))/(1-(1)/(5)xx(1)/(7))+tan^(-1)""((1)/(3)+(1)/(8))/(1-(1)/(3)xx(1)/(8))`
`=tan^(-1)""((7+5)/(35))/((35-1)/(35))+tan^(-1)""((8+3)/(24))/((24-1)/(24))`
`=tan^(-1)""(6)/(17)+tan^(-1)""(11)/(23)`
`=tan^(-1)""((6)/(17)+(11)/(23))/(1-(6)/(17)xx(11)/23)=tan^(-1)""((138+187)/(391))/((391-66)/(391))`
`=tan^(-1)""(325)/(325)=tan^(-1)1=(pi)/(4)=R.H.S.`
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