Solve the equation on the interval left bracket 0 comma 2 pi

Solve the equation on the interval left bracket 0 comma 2 pi right parenthesis[0, 2). 2sin^2theta+sintheta-1=0

Solution

2sin^2theta+sintheta-1=0

2sin^2 theta +2sintheta -sintheta -1=0

2sintheta(sintheta +1) -1(sintheta +1)=0

(2sintheta -1) (sintheta+1)=0

so (2sintheta -1)=0 or (sintheta+1)=0

sintheta =1/2 or sintheta = -1

theta = pi/6,5pi/6 , 3pi/2

theta ={pi/6,5pi/6 , 3pi/2 }