If the real part of the complex number z=(3+2 i cos θ)/(1-3 i cos θ), θ ∈(0, (π)/2) is zero, then the value of sin^2 3 θ+ cos^2 θ is equal to \ \ \ \.

If the real part of the complex number $\displaystyle z=\frac{3+2 i \cos \theta}{1-3 i \cos \theta}, \theta \in\left(0, \frac{\pi}{2}\right)$ is zero, then the value of $\displaystyle \sin ^2 3 \theta+\cos ^2 \theta$ is equal to \_\_\_\_.