Addition and Subtraction Formulas

$\displaystyle tan 60 + tan 225$

$\displaystyle \frac{tan60+tan225}{1-tan60 tan225}$

$\displaystyle \frac{\sqrt{3}+1}{1-\sqrt{3}\times1}$

$\displaystyle \frac{(\sqrt{3}+1)(1+\sqrt{3})}{1-\sqrt{3}}$

$\displaystyle \frac{2\sqrt{3}+4}{-2}$

The answer is suppose to be $\displaystyle -2-\sqrt{3}$

and im not gettin it can anyone help me?

Another question, What is the difference between $\displaystyle tan60+tan 225$ and $\displaystyle tan(60+225)$

because they give difference answers?