# 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.