If $$x \cos \theta+y \sin \theta=5, x \sin \theta-y \cos \theta=3$$, then the value of $$x^2+y^2=$$

If $$\sin \theta=-\frac{12}{13}, \cos \phi=-\frac{4}{5}$$ and $$\theta, \phi$$ lie in the third quadrant, then $$\tan (\theta-\phi)=$$

$$\frac{1-2\left[\cos 60^{\circ}-\cos 80^{\circ}\right]}{2 \sin 10^{\circ}}=\ldots \ldots$$

The value of $\sin 18^{\circ}$ is $\qquad$