Consider a circle with a radius of 7+sin(a) units centred at the origin for a in [0,1].

Now consider a triangle with one vertex at the origin, and two sides extending upwards such that the angle between the sides is 60 degrees.

The other two vertices of the triangle reach the edge of the circle. Another triangle is formed by reflecting this triangle across the x-axis.

Find the maximum remaining area inside the circle after subtracting the areas of both triangles for the largest possible given value of a The answer should be given in exact form (area, a).