Ugly trig equation for the first period of the sin function as its domain

so i stumbled across this unassuming equation:

2cot2x=secxsec(2pi/15)+2tan(2pi/15)

my solutions check out as 41/30pi and 11/30pi but i cant find more, is tehre a generalised form? as ive just basically found the arsine and arccos cases.