证明AB1垂直平面A1B1C1,求直线AC1与平面ABB1所成角的正弦值。---**Extraction Content:** **Question Stem:** 例 4. (18 浙江.) 如图，已知多面体 ABC-A₁B₁C₁，A₁A，B₁B，C₁C 均垂直于平面 ABC，∠ABC = 120°, A₁A = 4, C₁C = 1, AB = BC = B₁B = 2. (1) 证明：AB₁ ⊥ 平面 A₁B C₁； (2) 求直线 AC₁ 与平面 ABB₁ 所成角的正弦值. **Translation of Question Stem:** Example 4. (18 Zhejiang.) As shown in the figure, it is known that in the polyhedron ABC-A₁B₁C₁, A₁A, B₁B, and C₁C are all perpendicular to plane ABC, ∠ABC = 120°, A₁A = 4, C₁C = 1, AB = BC = B₁B = 2. (1) Prove that AB₁ ⊥ plane A₁B C₁; (2) Find the sine of the angle between the line AC₁ and the plane ABB₁. **Chart/Diagram Description:** * Type: 3D geometric figure depicting a polyhedron. * Main Elements: * Vertices: Labeled points A, B, C, A₁, B₁, C₁. * Lines: * Solid lines: AB, BC, A₁A, B₁B, C₁C, A₁B₁, B₁C₁, C₁A₁, AB₁, AC₁. * Dashed lines: AC, B₁C. * The figure represents a polyhedron with base triangle ABC and top triangle A₁B₁C₁. Vertical edges AA₁, BB₁, CC₁ connect the corresponding vertices. Line segments AB₁, AC₁, and B₁C are also shown. * Relative Position: Points A, B, C form the bottom base. Points A₁, B₁, C₁ form the top part, positioned above A, B, C respectively, connected by vertical lines.