An object is thrown with a velocity v at an angle \( \theta\) with the horizontal. Let the area enclosed by the curve of the projectile with the horizontal be A. For constant value of v the maximum value of A occurs at angle 'a' degrees and it is given by \(\frac { \sqrt { b } \times { v }^{ 4 } }{ { c\times g }^{ 2 } } \) where g is the acceleration due to gravity. Find \(a+b+c.\)

Details and assumptions.

1. a,b,c are integers.

2. b contains no factor which is a perfect square.

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