1．已知二面角α−l−β\alpha -l-\betaα−l−β的平面角为θ(0<θ<π2),A∈α,B∈β,C∈l,D∈l,AB⊥l\theta (0<\theta <\frac{\pi }{2}),A\in \alpha ,B\in \beta ,C\in l,D\in l,AB\bot lθ(0<θ<2π),A∈α,B∈β,C∈l,D∈l,AB⊥l，ABABAB与平面β\betaβ所成角为π3\frac{\pi }{3}3π．记ΔACD\Delta ACDΔACD的面积为S1S_{1}S1，ΔBCD\Delta BCDΔBCD的面积为S2S_{2}S2，则S1S2\frac{{S}_{1}}{{S}_{2}}S2S1的取值范围为((( )))