A trigonometric substitution

Geometry Level 4

\[ \large \frac 1 { \sin \left ( \frac \pi n \right ) } = \frac 1 { \sin \left ( \frac {2\pi} n \right ) } + \frac 1 { \sin \left ( \frac {3\pi} n \right ) } \]

Find the positive integer value of \(n>3 \) satisfying the equation above.