The equation tan((πx)/2) = √(3)/2 can be approached by first recognizing that tan(x) = √(3)/2 leads to x = π/6 + πn due to the periodic nature of the tangent function. To solve for x in the original equation, one can set πx/2 = π/6 + πn and then solve for x. This results in x = (2/π)(π/6 + πn), simplifying to x = 1/3 + 2n. An important correction noted is that tan(π/6) equals 1/√3, not √(3)/2, suggesting that using arctan(√(3)/2) is preferable for clarity. The discussion emphasizes the need to solve for x while addressing the nuances of the tangent function's values.
