Internal Triangle Area

Geometry Level 4

In triangle \(ABC\), \( \angle A = 100^\circ, \angle B = 60^\circ\) and \(BC\) has side length 1. Let \(D\) be the midpoint of side \(AC\), and \(E\) is a point on side \(BC\) such that \( \angle EDC = 80^\circ\). The value of \( [ABC] + 2 [CDE]\) can be expressed as \( \frac { \sqrt{a}} {b}\), where \(a\) and \(b\) are positive coprime integers. What is the value of \(a+b\)?

Note: \([PQRS]\) denotes the area of figure \(PQRS\).

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