Final answer:
To solve the equation tan(x + π/3) = √3/3 over the interval [0,3], subtract π/3 from both sides to isolate x and then use the inverse tangent function to find the values of x. The solutions are x = π/6 and x = 7π/6.
Step-by-step explanation:
To solve the equation tan(x + π/3) = √3/3 over the interval [0,3], we need to find the values of x that satisfy this equation. First, we need to isolate x by subtracting π/3 from both sides of the equation. This gives us tan(x) = √3/3 - π/3. Then, we can use the inverse tangent function to find the values of x. The inverse tangent of √3/3 - π/3 is equal to x. Since the domain of the tangent function is -π/2 to π/2, we need to find the values of x that fall within this interval. The solutions are x = π/6 and x = 7π/6.