cos(t) = x

8x^3 - 6x + 1 = 0

8cos(t)^3 - 6 * cos(t) + 1 = 0

2 * (4 * cos(t)^3 - 3 * cos(t)) + 1 = 0

2 * (4 * cos(t)^3 - 3 * cos(t)) = -1

4 * cos(t)^3 - 3 * cos(t) = -1/2

cos(3t) = -1/2

cos(3t) = cos(2pi/3 + 2pi * k) , cos(4pi/3 + 2pi * k)

3t = 2pi/3 + 2pi * k , 4pi/3 + 2pi * k

t = 2pi/9 + (2pi/3) * k , (4pi/9) + (2pi/3) * k

t = (2pi/9) + (6pi/9) * k , (4pi/9) + (6pi/9) * k

Assuming we want all values between t = 0 and t = 2pi

t = 2pi/9 , 8pi/9 , 14pi/9 , 4pi/9 , 10pi/9 , 16pi/9

t = 2pi/9 , 4pi/9 , 8pi/9 , 10pi/9 , 14pi/9 , 16pi/9

cos(t) = x

cos(2pi/9) , cos(4pi/9) , cos(8pi/9) , cos(10pi/9) , cos(14pi/9) , cos(16pi/9)

cos(16pi/9) = cos(2pi/9)

cos(14pi/9) = cos(4pi/9)

cos(10pi/9) = cos(8pi/9)

cos(2pi/9) , cos(4pi/9) , cos(8pi/9)

cos(2pi/9) = (1/4) * ((-4 + 4 * sqrt(3) * i)^(1/3) + (-4 - 4 * sqrt(3) * i)^(1/3))

cos(4pi/9) = 2 * cos(2pi/9)^2 - 1

cos(8pi/9) = 2 * cos(4pi/9)^2 - 1