Answer
$y-(\pi+3)=(3-3\sqrt 3)(x-\frac{\pi}{3})$
Work Step by Step
To find the equation of the tangent line, we first need the slope, which we can find by taking the derivative of $y=3x+6cosx$ using the power rule and trig function identities.
$$y'=3-6sinx$$
Using the point given, we can easily write the equation of the line in point-slope form $y-y_{1}=m(x-x_1)$ to get:
$y-(\pi+3)=(3-3\sqrt 3)(x-\frac{\pi}{3})$
