If tan(x/2) = Cosec x – sin x,then tan2(x/2) is equal to

Let tan(x/2)=tTherefore Sinx=2t/(1+t^2), Cosec x=(1+t^2)/2tThen the given expression will be reduced to:t=(1+t^2)/2t-2t/(1+t^2)t^4+4t^2-1=0Then we have to find out the value of t^2:Therefore, t^2=-2+√5,-2-√5 (By Shreedharacharya Method)But t^2 never less than 0 as it is a squareTherefore t^2=-2+√5 is the right oneHence tan^(X/2)=-2+√5