relation between tan theta and tan 2theta

I have got a question on the relation between $\displaystyle tan \theta$ and $\displaystyle tan 2 \theta$

The question consists of two parts:

The first pary asks me to solve the equation $\displaystyle a x^2 + 2 x - a = 0$

Then I 've got the correct ans, which is

[-1 + (1+a^2)^1/2]

_________________

a

or

[-1 - (1+a^2)^1/2]

_________________

a

Then the second part ask me to express $\displaystyle tan \theta$ in terms of $\displaystyle tan 2 \theta$ and the ans is

[-1 + (1+ (tan 2 theta) ^2 )^1/2]

___________________________________

a

or

[-1 - (1+ (tan 2 theta) ^2 )^1/2]

___________________________________

a