The positive integer value of n > 3 satisfying the equation 1sin⁡πn=1sin⁡2πn+1sin⁡3πn is ________.

1sin⁡πn−1sin⁡3πn=1sin⁡2πnor   sin⁡3πn−sin⁡πnsin⁡πnsin⁡3πn=1sin⁡2πnor   2sin⁡πncos⁡2πnsin⁡2πnsin⁡πnsin⁡3πn=1or   sin⁡4πn=sin⁡3πn⇒ 4πn+3πn=π⇒ n=7.