Find the value of :

tan² 30° + tan² 45° + tan² 60°

tan² 30° + tan² 45° + tan² 60°

$= \Big(\dfrac{1}{\sqrt3}\Big)^2 + (1)^2 + (\sqrt3)^2\\[1em] = \dfrac{1}{3} + 1 + 3\\[1em] = \dfrac{1}{3} + \dfrac{1 \times 3}{3} + \dfrac{3 \times 3}{3}\\[1em] = \dfrac{1}{3} + \dfrac{3}{3} + \dfrac{9}{3}\\[1em] = \dfrac{1 + 3 + 9}{3}\\[1em] = \dfrac{13}{3}\\[1em] = 4\dfrac{1}{3}$

Hence, tan² 30° + tan² 45° + tan² 60° = $4\dfrac{1}{3}$.