Geometry Level 5

$\large 4\sin { 27^\circ } =\sqrt { a+\sqrt { b } } -\sqrt { c-\sqrt { d } }$

Given that $$a,b,c$$ and $$d$$ are positive integers that satisfy the equation above with $$b$$ and $$d$$ are square free and at least $$2$$ of $$a,b,c,d$$ are equal, find $$a+b+c+d$$.

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