Step 1: Understand the problem. The goal is to evaluate the secant function for the given angles. Recall that secant is defined as the reciprocal of the cosine function: sec(x) = 1/cos(x).
Step 2: Start with the first term, sec(π/3). Use the unit circle to find cos(π/3). From trigonometric values, cos(π/3) = 1/2. Therefore, sec(π/3) = 1/(1/2).
Step 3: Next, evaluate sec(3π). Note that 3π is a multiple of π, and cosine values for multiples of π are either 1 or -1. Specifically, cos(3π) = -1. Thus, sec(3π) = 1/(-1).
Step 4: Combine the results from the previous steps. Substitute the evaluated values of sec(π/3) and sec(3π) into the expression to simplify further.
Step 5: Simplify the final expression to obtain the result. Ensure all fractions and radicals are simplified appropriately.