>>7
t=cos(θ+(π/6)) = cosθcos(π/6) - sinθsin(π/6)
= ((√3)/2)cosθ -(1/2)sinθ

2t = (√3)cosθ - sinθ
4t^2 = 3(cosθ)^2 + (sinθ)^2 - (√3) sin(2θ)
=2(cosθ)^2 - (√3) sin(2θ) + 1

2cos^2θ-(√3)sin2θ-(2a+1){(√3)cosθ-sinθ-1}=0

{4t^2 -1} - (2a+1) (2t -1) = 0

4t^2 - 2(2a+1)t + 2a = 0
t^2 -(a+(1/2))t +(a/2) = 0