Calculus of a Single Variable, Chapter 2, 2.4, Section 2.4, Problem 80

You need to find the equation of the tangent line to the given curve, at the point (pi/4,2), using the formula:
f(x) - f(pi/4) = f'(pi/4)(x - pi/4)
You need to notice that f(pi/4) = 2.
You need to evaluate the derivative of the given function, using chain rule, such that:
f'(x) = (2(tan x)^3)' => f'(x) = 2*3(tan x)^2*(tan x)'
f'(x) = 6tan^2 x*(1/(cos^2 x))
You need to evaluate f'(x) at x = pi/4 , hence, you need to replace pi/4 for x in equation of derivative:
f'(pi/4) = 6tan^2 (pi/4)*(1/(cos^2 (pi/4)))
f'(pi/4) = 6*1/(1/2) => f'(pi/4) = 12
You need to replace the values into equation of tangent line, such that:
f(x) - 2 = 12(x - pi/4) => f(x) = 12x - 3pi + 2
Hence, evaluating the equation of the tangent line to the given curve, at the given point, yields f(x) = 12x - 3pi + 2 .