Super Saiyan 3 is one of the most exciting transformations that Dragon Ball Z has. Goku first used this form in an attempt to stop Majin Buu and Bibidi, who were constantly searching for all the Z Fighters to destroy them.
Every detail of this transformation is Akira Toriyama's legendary achievement as a manga artist. The author showed the true image of a powerful mythical creature.
The Super Saiyan 3 transformation is one of Goku's greatest transformations. In this state, he has blonde hair and blue eyes like the other two Super Saiyan versions, but has the special feature that his hair grows much longer.
In addition, there is a special point that attracts everyone's attention, which is the “absence” of eyebrows. Not only happened to Goku, this also happened to Gotenks (Goten and Trunks's fused warrior), who also lost his facial eyebrows.
Author Akira Toriyama never specifically explains the reason why Super Saiyan 3 leaves the user without eyebrows. What the author does is describe his intention with the Super Saiyan transformation, which is largely intended to show the birth of an extremely wild and muscular creature.
So as Goku's muscles grew throughout his body, it caused even his face to “swell” in some spots. It's not that Goku lost his eyebrows, it's that they are not visible because he has gained muscles even in his face, for the purpose of expressing intense (controlled) anger so he can fight Fight with everything you have in a martial arts battle.
Super Saiyan 3 is a state that further distinguishes how much stronger Goku has become compared to Super Saiyan 2, and with the drastic change in appearance making this obvious, it can also manifests a more aggressive Super Saiyan form.