Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 168: 54

$x = 0.322+\pi~n$, where $n$ is any integer

The least positive x-intercept of the graph of this function is $x = 0.322$ Since the period of this function is $\pi$, the general form of the x-intercepts for the function are: $x = 0.322+\pi~n$, where $n$ is any integer. Therefore, the solutions of the equation $-2-cot(x-\frac{\pi}{4}) = 0$ are: $x = 0.322+\pi~n$, where $n$ is any integer