Answer
$\theta=\frac{3}{2}$ radians
Work Step by Step
Step 1: The formula to be used here will be $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of a sector of a circle of radius $r$ and central angle $\theta$.
Step 2: Substituting the values provided by the question into the formula, $3=\frac{1}{2}(2)^{2}\theta$
Step 3: $3=\frac{1}{2}\times(4)\times\theta$
Step 4: $3=2\times\theta$
Step 5: Multiplying both sides by $\frac{1}{2}$,
$3\times\frac{1}{2}=2\times\frac{1}{2}\times\theta$
Step 6: $\theta=\frac{3}{2}$ radians