If cos x = tany, cosy = tanz, cosz = tanx, then the value of sinx is

We have cos x= tany cos2⁡x=tan2⁡y=sec2⁡y−1=cot2⁡z−1  [∵cos⁡y=tan⁡z,sec⁡y=cot⁡z]⇒1+cos2⁡x=cot2⁡z=tan2⁡x1−tan2⁡x [∵cos⁡z=tan⁡x]=sin2⁡xcos2⁡x−sin2⁡x⇒ 2sin4⁡x−6sin2⁡x+2=0 or  sin2⁡x=3−52=5−122 or  sin⁡x=5−12=2sin⁡18∘