$x$ and $y$ are two complex numbers such that $|x|=|y|=1$.

If $\arg (x)=2 \alpha, \arg (y)=3 \beta$ and $\alpha+\beta=\frac{\pi}{36}$, then $x^6 y^4+\frac{1}{x^6 y^4}=$

If $x=a+b, y=a \alpha+b \beta, z=a \beta+b \alpha$ and $\alpha, \beta$ are the complex cube roots of unity, then $x^3+y^3+z^3=$

If $z=\frac{3+2 i \cos \theta}{1-2 i \sin \theta}$ is a purely imaginary number, then

$$ \sin ^2 \theta+\cos ^2 3 \theta= $$