To simplify the equation, we can first use the trigonometric identity cos(π - x) = -cos(x):

√3 cos(π + 2.5x) - cos(π/2 - 2.5x) = 0

Next, cos(π + 2.5x) = -cos(2.5x) and cos(π/2 - 2.5x) = sin(2.5x):

√3 (-cos(2.5x)) - sin(2.5x) = 0

-√3 cos(2.5x) - sin(2.5x) = 0

To solve this trigonometric equation, we need to find the values of x that satisfy it. There could be multiple solutions within a specific interval.