If 6 tan2θ - 2 = 0, find the value of 3sinθ + cos2(1.5θ)

6 tan²θ - 2 = 0

tan²θ = \(\frac{2}{6}\) = \(\frac{1}{3}\)

tanθ = \(\frac{1}{\sqrt {3}}\)

θ = 30°

Now,

⇒ 3sinθ + cos²(1.5θ) = 3 × \(\frac{1}{2}\) + cos²(45°)

= \(\frac{3}{2}\) + \(\frac{1}{2}\)  = 2