Find the value of theta in the diagram - JAMB Mathematics 2001 Question

Using cosine formula (t\(\sqrt{3}\))² = t² + t² - 2t² cos\(\theta\)

3t² = 2t² - 2t² cos\(\theta\) = 2t²(1 - cos\(\theta\))

1 - cos\(\theta\) = \(\frac{3t^2}{2t^2}\) = \(\frac{3}{2}\)

cos = 1 - \(\frac{3}{2} = -\frac{1}{2}\)

\(\theta\) = cos^-1(-\(\frac{1}{2}\)) = 120^o and 240^o

N.B 0 \(\geq\) \(\theta\) 360