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Answer 1 · 2017-03-07T15:50:28

#3sin^2theta-sinthetacostheta-4cos^2theta=0#

#=>(3sin^2theta)/cos^2theta-(sinthetacostheta)/cos^2theta-(4co s^2theta)/cos^2theta=0#

#=>3tan^2theta-tantheta-4=0#

#=>3tan^2theta-4tantheta+3tantheta-4=0#

#=>tantheta(3tantheta-4)+1(3tantheta-4)=0#

#=>(3tantheta-4)(tantheta+1)=0#

When

#3tantheta-4=0#

#=>tantheta=4/3=tan(tan^-1(4/3))#

#=>theta=npi+tan^-1(4/3)" where "n in ZZ#

When

#tantheta+1=0#

#=>tantheta=-1=tan(-pi/4)#

#=>theta=npi-pi/4" where "n in ZZ#