How do i solve this trigonometry question? (section 7.3)

Solve: 

Now, a tangent function is an odd function, and you can find the proof on the internet, so we can say that:




Now, we just need to find what is.
Since is not an exact angle, we need to manipulate it in some way that it will be yield exact values.



Thus, we can say:


Using difference formula to simplify the expression, we know that the difference formula states:



The exact value for
The exact value for

Thus:



Rationalise the denominator:



Expand the perfect square: