Solve the equation on the interval 0 ≤ θ < 2π.

2 cos ^2 θ - 3 cos θ + 1 = 0

would really appreciate answer for this.

{0, π/3, 5π/3}

Step-by-step explanation:

Let x = cos θ. Then:

2x² - 3x + 1 = 0

x = (3 ± 1)/4

x1 = 1, x2 = 1/2

If cos θ = 1, then θ = 0

If cos θ = 1/2, then θ = π/3 or 5π/3

Take A  which is the point (1,1)
180 degree rotation takes it to (-1,-1)
Translation takes that to (-1+5, -1)  = (4,-1)
Then translation of 1 unit down   gives  the  final point at (4, -1-1) = (4,-2) = A'

If you pefrorm the same process for points B, C and  D you'll get the final answer.

The 180 rotation for B , C and D will take them to (-5,-4) , (-7,-1 ) and (-3, 2) 
respectively.