# Normal trigonometry would take too long

Geometry Level 4

$\sin(1^\circ)\cdot \sin(2^\circ)\cdot \sin(3^\circ)\cdot\cdot\cdot \sin(88^\circ)\cdot \sin(89^\circ) = a\cdot\left ( \frac{b}{2^{\,a\cdot c}} \right )^{\frac{1}{2}}$

The equation above holds true, where $$a$$, $$b$$ and $$c$$ are prime numbers. Evaluate $$25\cdot (a\cdot c)-(480\cdot b+3\cdot a)$$.

Note: After getting the answer, try to express it in the given form.

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