Each of the two triplets of numbers $\displaystyle (a, b, c)\ \& \left(\frac{a}{2b},\ \frac{2b}{3c},\ \frac{3c}{a}\right)$ is a Geometric Progression. Can the numbers $\displaystyle a,b,c$ be the lengths of the sides of a triangle? If they can what triangle is it? Find the angles of the triangle.