Step 1 :We are given the formula \(\omega=\frac{\theta}{t}\) and we need to find the value of t. We can rearrange the formula to solve for t as follows: \(t=\frac{\theta}{\omega}\).
Step 2 :We can then substitute the given values of \(\theta\) and \(\omega\) into the formula to find the value of t.
Step 3 :Substituting the given values, we get \(t=\frac{2 \pi/3}{3 \pi/7}\).
Step 4 :Simplifying the above expression, we get \(t=\frac{14}{9}\).
Step 5 :Final Answer: \(\boxed{\frac{14}{9}}\) minutes.