Solve the trigonometric equation for all values $0 \leq x<2 \pi$. \[ \cot x+1=0 \]

Step 1 ：Rewrite the equation as: \( \frac{1}{\tan x} + 1 = 0 \)

Step 2 ：Solve for \(\tan x\) to get \(\tan x = -1\)

Step 3 ：Find the value of x in the range \(0 \leq x < 2\pi\) that satisfies the equation: \(x = \frac{3\pi}{4}\)

Step 4 ：\(\boxed{x = \frac{3\pi}{4}}\)