Answer
The equation of the tangent line is $y=2\sqrt{3}x+\dfrac{6-2\sqrt{3}\pi}{3}$.
Work Step by Step
$f'(x)=\dfrac{d}{dx}\sec{x}=\sec{x}\tan{x}$
$f'(\frac{\pi}{3})=(\sec{\frac{\pi}{3}})(tan{\frac{\pi}{3}})=2\sqrt{3}.$
Equation of tangent: $(y-y_0)=m(x-x_0)$ at point $(x_0, y_0)$ and slope $m$.
$(y-2)=2\sqrt{3}(x-\frac{\pi}{3}) \rightarrow y=2\sqrt{3}x+\dfrac{6-2\sqrt{3}\pi}{3}$
