You're well on your way to solving this, and closer to the solution than you think !
-- To work with the y-components of the velocities, use the sines of the
angles, not the cosines. The cosines are the horizontal components.
-- Make that change in your last line.
Make the 3v₂ term negative ... the vertical part of v₂ is downward.
-- The m₁ had no vertical momentum before the collision,
so the sum of all vertical components after the collision is still zero.
Set your last line equal to zero, and it'll practically solve itself for v₂ .
