If $\cos x=\tan y$, $\cos y=\tan z$, $\cos z=\tan x$, then find the value of $\sin x$
My reference says $\sin x=2\sin 18^\circ$, but how do I approach the problem ?
My Attempt $$ \sin x=\tan x.\cos x=\tan x.\tan y $$ $$ \tan^2z=\cos^2y=\frac{1}{1+\tan^2y}=\frac{1}{1+\cos^2x}\\ \tan^2y=\cos^2x=\frac{1}{1+\tan^2x}=\frac{1}{1+\cos^2z} $$ I have no clue of whats the trick to solve this.