# Doubly Trisected Triangle

**Geometry**Level 5

Triangle ABC has \(\angle A = 40^{\circ}\), \(\angle B = 60^{\circ}\), \(\angle C = 80^{\circ}\). Points \(M,N\) trisect the side \(BC\) and points \(P,Q\) trisect the side \(AC\). The lines \(AM, AN, BP, BQ\) intersect at the points \(S,T,U,V\) as shown in the figure below, dividing the triangle into 9 regions. Determine the smallest possible value of \([ABC] + [STUV]\) such that both \([ABC]\) and \([STUV]\) are positive integers.

**Details and assumptions**

\([PQRS]\) refers to the area of figure \(PQRS\).

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