From one of singapore's poly, and don't know how to do math

Question

sin θ + square root 2 = -sin θ

3 tan²x - 1 = 0

2 sin²θ - sin θ - 1 = 0

Answer 1

Get sinθ to the left, and sqrt(2) to the right:

2 sin θ = -sqrt(2)

Devide by 2:

sin θ = -sqrt(2)/2

This is the reference angle π/4 in IV and III quadrants.

So the solution is

-π/4 + 2πk

and

5π/4 + 2πk

k=0,+-1, +-2 ...