What is $$\mathop {Lim}\limits_{\theta \to 0} {{\sin \theta } \over \theta }\,\,$$ equal to ?

Eigen values of a real symmetric matrix are always

Consider the following system of equations
$$2{x_1} + {x_2} + {x_3} = 0,\,\,{x_2} - {x_3} = 0$$ and $${x_1} + {x_2} = 0.$$
This system has

A series expansion for the function $$\sin \theta $$ is _______.