(1)
f(x) = a.b
=（√3cosx/2,2cosx/2）.（2cosx/2,-sinx/2）
= 2√3(cosx/2)^2 - sinx
f（θ）=√3+1
√3+1 = 2√3(cosθ/2)^2 - sinθ
= √3( cosθ +1) - sinθ
1= √3cosθ - sinθ
1/2= (√3/2)cosθ - (1/2)sinθ
= sin(π/3+θ)
π/3+θ = π/6
θ = -π/6
(2) To be continued. .