Answer 1

сtgx+3tgx+4=0
1/tgx+3tgx+4=0
3tg²+4tgx+1=0,tgx≠0
tgx=a
3a²+4a+1=0
D=16-12=4
a1=(-4-2)/6=-1⇒tgx=-1⇒x=-π/4+πn,n∈Z
a2=(-4+2)/6=-1/3⇒tgx=-1/3⇒x=-arctg1/3+πn,n∈Z