Answer
$= (2-\sqrt(3))$
Work Step by Step
$tan(15) = tan(60-45)$
$= \frac{[tan(60)-tan(45)]}{[1+tan(60)\times tan(45)]}$
$=\frac{[\sqrt(3)-1]}{[1+\sqrt(3)*1]}$
Multiply numerator and denominator by $(1-\sqrt(3))$ to get
$= [-(1-\sqrt(3))^2]/(1-3)$
$= (1-2\sqrt(3)+3)/2$
$= (4-2\sqrt(3))/2$
$= (2-\sqrt(3))$