Trigonometric problem using basic trigonometry 
If $x$ is a solution of the equation: $$\tan^3 x = \cos^2 x - \sin^2 x$$
  Then what is the value of $\tan^2 x$?

This is the problem you are supposed to do it just with highschool trigonometry , but i can't manage to do it please help
Here are the possible answers:
$$a) \sqrt{2}-1, b) \sqrt{2}+1, c) \sqrt{3}-1, d) \sqrt{3}+1, e)\sqrt{2}+3$$

Hint: $$(1+\tan^2 x)^2 (\tan^2 x)^3 = \left((1+\tan^2 x) (\tan^3 x)\right)^2 = \left( \frac{1}{\cos^2 x} (\cos^2 x - \sin^2 x) \right)^2 = \left( 1 - \tan^2 x\right)^2.$$ 
