Step 1 :Let's denote the measure of the equal angles in an isosceles triangle as \(x\) and the measure of the remaining angle as \(y\).
Step 2 :According to the problem, \(x = 2y\).
Step 3 :Also, the sum of the angles in a triangle is equal to \(\pi\) radians. Therefore, we have the equation \(2x + y = \pi\).
Step 4 :Substituting \(x = 2y\) into this equation, we can solve for \(y\) and then find \(x\).
Step 5 :The solution to the system of equations is \(x = \frac{2\pi}{5}\) and \(y = \frac{\pi}{5}\).
Step 6 :This means that the measure of the equal angles in the triangle is \(\frac{2\pi}{5}\) radians and the measure of the remaining angle is \(\frac{\pi}{5}\) radians.
Step 7 :Final Answer: The exact radian measures of the three angles in the triangle are \(\boxed{\frac{2\pi}{5}}\), \(\boxed{\frac{2\pi}{5}}\), and \(\boxed{\frac{\pi}{5}}\).