Primes can make answers Creative @BrilliantGeometry Level 4
The value of \[ 2 \sin 2°+ 4 \sin 4°+ 6 \sin 6°+ ......+ 180 \sin 180°\] is \( P•Q(R°)\), where \(P\) and \(R\) are integers, and \( Q \) is a trigonometric function.
If \( Q \) is \( \csc\), let \(S = 2 \).
If \( Q \) is \( \sec \), let \(S = 3 \).
If \( Q \) is \( \cot \), let \( S = 5 \).
What is the value of \( ( P + R) \times S \)?
Note: \(R\) is an integer from 0 to 90.