Find $x$ and $y$ If $\frac{\tan 8°}{1-3\tan^{2}8°}+\frac{3\tan 24°}{1-3\tan^{2}24°}+\frac{9\tan 72°}{1-3\tan^{2}72°}+\frac{27\tan 216°}{1-3\tan^{2}216°}=x\tan 108°+y\tan 8°$, find x and y. I am unable to simplify the first and third terms. I am getting power 4 expressions. Thanks.

HINT:
$$\tan(3\cdot8^\circ)=\dfrac{3\tan 8^\circ-\tan^38^\circ}{1-3\tan^28^\circ}$$
Now, $$\frac{\tan 8^\circ}{1-3\tan^28^\circ}-y\tan8^\circ=\dfrac{(1-y)\tan 8^\circ-(-3y)\tan^38^\circ}{1-3\tan^28^\circ}$$ which will be a multiple of $\tan(3\cdot8^\circ)$ if
 $$\dfrac{1-y}{-3y}=\dfrac31\iff y=-\dfrac18$$
$$\implies\frac{\tan A}{1-3\tan^2A}-\left(-\dfrac18\right)\tan A=\dfrac38\tan3A$$
and I should leave it here.
