tan -105 degrees
Edit: Never mind I got it, the answer is 2+2radical3, correct?
Edit 2: Forgot to cancel the 2 before the radical, so it's 2+radical 3...
An angle of $\displaystyle \displaystyle 105^{\circ}$ in the clockwise direction is the same as an angle of $\displaystyle \displaystyle 255^{\circ}$ in the anticlockwise direction.
So $\displaystyle \displaystyle \tan{\left(-105^{\circ}\right)} = \tan{\left(255^{\circ}\right)}$
$\displaystyle \displaystyle = \tan{\left(180^{\circ} + 75^{\circ}\right)}$
$\displaystyle \displaystyle = \tan{\left(75^{\circ}\right)}$ since the tangent values are the same in the first and third quadrants...
$\displaystyle \displaystyle = \tan{\left(30^{\circ} + 45^{\circ}\right)}$.
Now make use of the identity $\displaystyle \displaystyle \tan{\left(\alpha + \beta\right)} \equiv \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}$.