Answer
$0.3649,1.2059, 3.5065, 4.3475$; graph (a)
Work Step by Step
Step 1. Solving the equation for $tan(x)$, we have $tan(x)=\frac{3\pm\sqrt {5}}{2}$ or $tan(x)=0.3820$ and $tan(x)=2.6180$
Step 2. For $tan(x)=0.3820$, we can find the solutions in $[0,2\pi)$ as $x_0=tan^{-1}0.3820\approx0.3649$ and $x=\pi+x_0\approx3.5065$
Step 3. For $tan(x)=2.6180$, we can find the solutions in $[0,2\pi)$ as $x_0=tan^{-1}2.6180\approx1.2059$ and $x=\pi+x_0\approx4.3475$
Step 4. With the above zeros, we can identify, based on the distances between zeros, the corresponding graph as (a).
