Limits Continuity And Differentiability

If \(\mathop {\lim }\limits_{x \to 0} {[1 + x\ln (1 + {b^2})]^{1/x}} = 2b{\sin ^2}\theta\), \(b > 0\) and \(\theta \in ( - \pi ,\pi ]\), then the value of \(\theta\) is