# Maximum value#3

Geometry Level 4

$D=\frac { \sqrt [ 3 ]{ \sin A } +\sqrt [ 3 ]{ \sin B } +\sqrt [ 3 ]{ \sin C } }{ \sqrt [ 3 ]{ \cos\frac { A }{ 2 } } +\sqrt [ 3 ]{ \cos\frac { B }{ 2 } } +\sqrt [ 3 ]{ \cos\frac { C }{ 2 } } }$

If $$A$$, $$B$$ and $$C$$ in the equation above are 3 angles of the triangle $$ABC$$, find the maximum value of $$D$$.

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