Prove that: `"cot"pi/(24)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)`

Explanation

`cot (pi/24) = cos (pi/24)/sin(pi/24)`

`=cos (pi/24)/sin(pi/24)**(2cos(pi/24))/(2cos(pi/24))`

`=(2cos^2 (pi/24))/(2sin(pi/24)cos(pi/24))`

`=(1+cos(pi/12))/(sin(pi/12))`

`=(1+cos(pi/4-pi/6))/(sin(pi/4-pi/6))`

`=(1+cos(pi/4)cos(pi/6)+sin(pi/4)sin(pi/6))/(sin(pi/4)cos(pi/6)-cos(pi/4)sin(pi/6))`

`=(1+(1/sqrt2)(sqrt3/2)+(1/sqrt2)(1/2))/((1/sqrt2)(sqrt3/2)-(1/sqrt2)(1/2))`

`=(2sqrt2+sqrt3+1)/(sqrt3-1)`

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