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Prove that tan^(-1).(1)/(sqrt2) + sin^(-...

Prove that `tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10) = -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2))`

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`tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10)`
`= tan^(-1).(1)/(sqrt2) + tan^(-1).(1)/(2) - tan^(-1) 3`
`= tan^(-1).(1)/(sqrt2) -[tan^(-1) 3 - tan^(-1).(1)/(2)]`
`= tan^(-1).(1)/(sqrt2) - [tan^(-1).(3- (1)/(2))/(1 + (3)/(2))]`
`= tan^(-1).(1)/(sqrt2) - tan^(-1) 1`
`= tan^(-1).((1)/(sqrt2) -1)/(1 + (1)/(sqrt2))`
`= tan^(-1) (1 - sqrt2)/(1 + sqrt2)`
`= -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2)) " " ( :' (1 - sqrt2)/(1 + sqrt2) lt 0)`
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