Question:
If the real part of the complex number
$\mathrm{z}=\frac{3+2 i \cos \theta}{1-3 i \cos \theta}, \theta \in\left(0, \frac{\pi}{2}\right)$ is zero, then the value
of $\sin ^{2} 3 \theta+\cos ^{2} \theta$ is equal to______________
Solution:
$\operatorname{Re}(z)=\frac{3-6 \cos ^{2} \theta}{1+9 \cos ^{2} \theta}=0$
$\Rightarrow \theta=\frac{\pi}{4}$
Hence, $\sin ^{2} 3 \theta+\cos ^{2} \theta=1$