An Angle from the Unfolded Net of a Tetrahedron

The figure shows the planar unfolding (net) of a tetrahedron $P$-$ABC$, in which $D$, $E$, and $F$ mark the positions taken by the apex $P$ when the faces are unfolded. Given that $AC=1$, $AB=AD=\sqrt 3$, $AB\perp AC$, $AB\perp AD$, and $\angle CAE=30^\circ$, find $\cos\angle FCB$.