JEE Advance - Mathematics (1988 - No. 12)

$$\left| {\matrix{ {1 + {{\sin }^2}\theta } & {{{\cos }^2}\theta } & {4\sin 4\theta } \cr {{{\sin }^2}\theta } & {1 + {{\cos }^2}\theta } & {4\sin 4\theta } \cr {{{\sin }^2}\theta } & {{{\cos }^2}\theta } & {1 + 4\sin 4\theta } \cr } } \right| = 0$$ are