A sequence of triangles is defined as follows:
\( T_1\) is an isosceles triangles inscribed in a given circle. With one of the equal sides of \(T_1\) as the base , \( T_2\) is an isosceles triangles inscribed in the circle so that the non-coincident vertices of \( T_1\) and \(T_2\) are on the same arc. Similarly successive isosceles triangles are drawn with preceding triangle's equal side as base . Proceeded this way till infinitum . Prove that as \( n \to \infty\) , \(T_n \to \) an equilateral triangle.