(2)①∵aa 1=a 1a2=a2a3= 1,a 1a2⊥a2a3

∴θ2=45 ,

θ = 22.5.(2 points)

So the answer is 22.5;

②

∵aa 1=a 1a2=a2a3= 1,a 1a2⊥a2a3，

∴A 1A3= 2，AA3= 1+ 2。

And ∵A2A3⊥A3A4,

∴A 1A2∥A3A4.

Similar: a3 a4∑a5 a6,

∴∠A=∠AA2A 1=∠AA4A3=∠AA6A5，

∴AA3=A3A4,AA5=A5A6

∴a2=A3A4=AA3= 1+ 2, (3 points)

a3=AA3+A3A5=a2+A3A5。

A3A5 = 2 a2，

∴a3=a5a6=aa5=a2+ 2 a2 =(2+ 1)2。

∴an=( 2+ 1)n- 1； (5 points)

(3)∫a 1 a2 = aa 1

∴θ 1=∠A2A 1A3=2θ，

∴θ2=∠A2A4A3=θ+2θ=3θ，

∴θ3=∠A2A4A3+θ=4θ，

So the answer is θ 1=2θ, θ2=3θ, θ 3 = 4θ;

(4) According to the meaning of the question: θ 4 = 4θ ≤ 90, θ 5 = 5θ > 90,

∴ 18