Mistakes give rise to Problems- 11

Geometry Level 4

In maths we see the following property for multiplication of numbers,\[\color{Green}{a(b\times c) = b\times a(c)}\]

But if you do that here, \[\sin (3\times a) = 3\times \sin (a)\] then it will be a \(\color{Red}{\textbf{Big Mistake !!!}}\)

But for how many angles \(\color{Blue}{a}\) such that \(-100\leq a \leq 100\), is the above said "false" property seen to be "true" ?

Details and assumptions:-

Angle measuring \(\color{Blue}{a}\) is actually measuring " \(\color{Blue}{a}\) radians"

This problem is a part of my set Mistakes Give Rise to Problems

Excel in math and science