To solve the problem tan \theta + 3 \cot \theta = 2\sqrt{3} for 0° < \theta < 90°, we need to find the value of \theta.

1. First, recall the trigonometric identities:
   • \tan \theta = \frac{\sin \theta}{\cos \theta}
   • \cot \theta = \frac{\cos \theta}{\sin \theta}
2. Substitute these identities into the equation:
   \frac{\sin \theta}{\cos \theta} + 3 \cdot \frac{\cos \theta}{\sin \theta} = 2\sqrt{3}
3. Clear the fractions by multiplying through by \sin \theta \cos \theta:
   \sin^2 \theta + 3 \cos^2 \theta = 2 \sqrt{3} \sin \theta \cos \theta
4. Recall the Pythagorean identity: \sin^2 \theta + \cos^2 \theta = 1.
   Rewrite the equation:
   1 + 2 \cos^2 \theta = 2 \sqrt{3} \sin \theta \cos \theta
5. Convert to a single trigonometric function using:
   \sin(2\theta) = 2 \sin \theta \cos \theta
   Rearrange:
   \cos^2 \theta - \sqrt{3} \sin \theta \cos \theta + \frac{1}{2} = 0
6. Assume possible value for \theta based on options given. Let's check \theta = 60^\circ.
7. Evaluate the equation for \theta = 60^\circ:
   • \sin 60° = \frac{\sqrt{3}}{2}
   • \cos 60° = \frac{1}{2}
   • Calculate \tan 60° = \frac{\sqrt{3}/2}{1/2} = \sqrt{3}
   • Calculate \cot 60° = \frac{1/2}{\sqrt{3}/2} = \frac{1}{\sqrt{3}}
   • Substitute back into the original equation:
     \sqrt{3} + 3 \cdot \frac{1}{\sqrt{3}} = 2\sqrt{3}
     2\sqrt{3} = 2\sqrt{3} (True)
8. Hence, the value of \theta that satisfies the equation is 60°.