Question

How do you solve `tan (theta/8) + √3 = 0`?

Answer 1

If `tan(theta/3) + sqrt(3) =0`
then
`color(white)("XXXX")` `tan(theta/8) = -sqrt(3)`

and `(theta/8) = -30^@` or `150^@` (it's one of the standard trigonometric triangles)

Therefore
`color(white)("XXXX")` `theta = 8*(-30^@) = 240^@ = 120^@`
or
`color(white)("XXXX")` `theta = 8 *(150^@) = 1200^@ = 120^@`

In either case `theta` is equivalent to `120^@`