an error again in dcp

looks like i am a genius in finding errors

two silts are sep by 0.32mm .A beam of 500nm strinkes the solts producing an interference pattern . Determine the interference pattern between angular range -30egreees<0<30degrees

my way since it is 30 degree that means that the angle is not so small that sin@=tan@
i assume
dsintheta =n l ambda
so we know the phase n

thats wat i thought

but in the book its simply given
since the fring width=x)which is derived for small angles)
they find it out dont u think its wrong ..........