4sin3x+1=9co3x
8sin3x/2 * cos3x/2 +sin²3x/2 + cos²3x/2 -9cos²3x/2 + 9sin²3x/2=0
10sin²3x/2 + 8sin3x/2 * cos3x/2 -8cos²3x/2=0 / cos²3x/2≠0
10tg²3x/2+8tg3x/2-8=0
tg3x/2=a
10a²+8a-8=0
D=64+320=384 √D=8√6
a1=(-8-8√6)/20=(-2-2√6)/5⇒tg3x/2=(-2-2√6)/5⇒3x/2=-arctg(2+2√5)/5+πn⇒
⇒x=-2/3arctg(2+2√5)/5+2πn/3
a2=(-8+8√6)/20=(-2+2√6)/5⇒tg3x/2=(-2+2√6)/5⇒3x/2=arctg(-2+2√5)/5+πn⇒
⇒x=2/3arctg(-2+2√5)/5+2πn/3