Let △ABC be an equilateral triangle. Points D,E,F are drawn on sides AB,BC, and CA respectively such that [ADF]=[BED]+[CEF] and △ADF∼△BED∼△CEF. The ratio [DEF][ABC] can be expressed as da+bc , where a, b, c, and d are positive integers such that a and d are relatively prime, and c is not divisible by the square of any prime. Find a+b+c+d.
(Here [P] denotes the area of polygon P.)