To solve the inequality:

Cos((3/2)x)cos(x/2) - 1 > ((1 - sqrt(3))/2) * cos(x)

Let's simplify the left side first:

Cos((3/2)x)cos(x/2) - 1 = cos(3x/2) cos(x/2) - 1
= (cos^2(x/2) - sin^2(x/2)) cos(x/2) - 1
= cos^3(x/2) - cos(x/2) - 1

Now the inequality becomes:

cos^3(x/2) - cos(x/2) - 1 > ((1 - sqrt(3))/2) * cos(x)

Substitute y = cos(x/2), then the inequality becomes:

y^3 - y - 1 > ((1 - sqrt(3))/2) * 2y
y^3 - y - 1 > (1 - sqrt(3))y

Now, we need to solve this cubic inequality, which is a bit more complex. By graphing or using numerical methods, we can find the solutions.