Find the equation of the tangent line to the curve $y=2 \tan x$ at the point $\left(\frac{\pi}{4}, 2\right)$. The equation of this tangent line can be written in the form $y=m x+b$ where $m$ is: and where $b$ is:

Step 1 ：Given the function \(y = 2 \tan x\), we need to find the equation of the tangent line at the point \(\left(\frac{\pi}{4}, 2\right)\).

Step 2 ：The equation of a tangent line to a curve at a given point can be found using the formula \(y = mx + b\), where \(m\) is the slope of the tangent line and \(b\) is the y-intercept.

Step 3 ：The slope of the tangent line is the derivative of the function at the given point. So, first we need to find the derivative of the function \(y = 2 \tan x\).

Step 4 ：The derivative of \(y = 2 \tan x\) is \(2 \sec^2 x\). Evaluating this at \(x = \frac{\pi}{4}\) gives \(m = 4\).

Step 5 ：Now, we need to find the y-intercept, \(b\). We can use the point-slope form of a line, \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is the point of tangency, and solve for \(b\).

Step 6 ：Substituting \(m = 4\), \(x_1 = \frac{\pi}{4}\), and \(y_1 = 2\) into the equation gives \(b = - \frac{1}{2} + \frac{\pi}{4}\).

Step 7 ：\(\boxed{m=4}\) and \(\boxed{b= - \frac{1}{2} + \frac{\pi}{4}}\). Therefore, the final answer is \(\boxed{m=4}\) and \(\boxed{b= - \frac{1}{2} + \frac{\pi}{4}}\).