Answer
$$θ=\frac{\pi }{9}$$
Work Step by Step
Solving the equation using inverse trigonometric functions, we find:
$$2\cos \left(3θ\right)=1,\:0\le \:θ\le \frac{\pi }{2} \\ \cos \left(3θ\right)=\frac{1}{2} \\ θ=\frac{\pi }{9}+\frac{2\pi n}{3},\:θ=\frac{5\pi }{9}+\frac{2\pi n}{3} \\ θ=\frac{\pi }{9}$$