Find the value of:

cos² 60° + sec² 30° + tan² 45°

$\text{cos}^2 60° + \text{sec}^2 30° + \text{tan}^2 45° = \Big(\dfrac{1}{2}\Big)^2 + \Big(\dfrac{2}{\sqrt3}\Big)^2 + (1)^2\\[1em] = \dfrac{1}{4} + \dfrac{4}{3} + 1\\[1em] = \dfrac{1 \times 3}{4 \times 3} + \dfrac{4 \times 4}{3 \times 4} + \dfrac{1 \times 12}{12}\\[1em] = \dfrac{3}{12} + \dfrac{16}{12} + \dfrac{12}{12}\\[1em] = \dfrac{3 + 16 + 12}{12}\\[1em] = \dfrac{31}{12}\\[1em] = 2\dfrac{7}{12}$

Hence, cos² 60° + sec² 30° + tan² 45° = $2\dfrac{7}{12}$.