Coincident roots means two real and equal roots.

Then discriminant $(b^2-4ac)=0$

Then, $\bigg[2.(a+1)\bigg]^2-4\cdot a^2 \cdot 4=0$

$\Rightarrow 4a^2+8a+4=16a^2$

$\Rightarrow 12a^2-8a-4=0$

$\Rightarrow 3a^2-2a-1=0$

$\Rightarrow 3a^2-3a+a-1=0$

$\Rightarrow 3a(a-1)+(a-1)=0$

$\Rightarrow (a-1)(3a+1)=0$

Then, $a=1,-\frac 13$