A 12 inch diameter round pizza

has been sliced by 3 straight cuts, leaving a right triangle in the middle as shown here

The edge of the pizza has been cut into 6 arcs, one each of the following, in degrees, totaling 360 degrees:

\[{15, 30, 45, 60, 90, 120}\]

but not necessarily in that order. The maximum area, in square inches, this right triangle piece in the middle can have can be expressed as

\(\dfrac { 1 }{ a } (b+c\sqrt { 2 } +d\sqrt { 3 } +e\sqrt { 6 } )\)

where \(a, b, c, d, e\) are integers (which may be negative). Find \(a+b+c+d+e\).

Integer \(a\) is positive. Do not rely on diagram to guess arcs in degrees.

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