Circle-ception: The next level

Geometry Level 4

A sector of a circle of radius 1010 and subtended angle 60°60° has a circle inscribed in it - its diameter can be written as ab\frac { a }{ b } , where aa and bb are co-prime integers.

Find the value ofa2b2a+b\left\lceil \frac { { a }^{ 2 }b^{ 2 } }{ a+b } \right\rceil

Part 1: Circle-ception.
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