(a) At what point does the curve $$x=1-2\cos^2(t),\;\;y=\tan(t)(1-2\cos^2(t))$$ cross itself?

$(x, y) =$ (, )

(b) At the point where the above curve crosses itself, find the equations of both tangent lines. List them in order of increasing slope.

Tangent line with smaller slope: $y =$

Tangent line with larger slope: $y =$