1. Given,  1- (1- cos²T)      =  sin²T +1
                           tan²t

        1-     (sin ² T)               = sin²T + 1
                  sin²T/cos²T

         1-cos ²T  = 1+ sin²T

-Cos²T = sin²T (this is not identical)

2. So square both sides : Cos⁴T = Sin⁴T

3 . Cos⁴T - Sin⁴T =0

4. (cos²T-sin²T) (cos²2T+sin²T)=0

5. That gives you value of Theta as 45 degree. Am I right?

Where T=Theta.