relation between tan theta and tan 2theta

I have got a question on the relation between [LaTeX ERROR:
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and [LaTeX ERROR:
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The question consists of two parts:

The first pary asks me to solve the equation [LaTeX ERROR:
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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 [LaTeX ERROR:
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in terms of [LaTeX ERROR:
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and the ans is

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

___________________________________

a

or

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

___________________________________

a