Find the value of `tan(1/2cos^-1(sqrt5/3))`

Explanation

`tan[ 1/2 cos^-1(sqrt5/3)]`

`1/2 cos^-1(sqrt5/3) = theta`

`cos^-1(sqrt5/3) = 2 theta`

`cos 2theta = sqrt5/3`

`(1- tan^2 theta)/(1 + tan^2 theta) = sqrt5/3`

`3- 3 tan^2 theta = sqrt5 + sqrt5 tan^2 theta`

`sqrt((3 - sqrt5)/(3 + sqrt5))= tan theta`

`sqrt(((3- sqrt5)(3- sqrt5))/((3 + sqrt5)(3- sqrt5))) = tan theta`

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