Answer:
x = 3/2π
Explanation:
You know that tan(θ) = 0 for θ = nπ and any integer n. This means ...
tan(x/3 +π/2) = 0
x/3 +π/2 = nπ
x/3 = (n -1/2)π . . . . . subtract π/2
x = 3(n -1/2)π . . . . . multiply by 3
In the range 0 < x < 2π, the value for n=1 is relevant:
x = 3/2π