Are the functions $f, g,$ and $h$ given below linearly independent? $$f(x) = 0, \ \ \ \ g(x) = \cos\!\left(3x\right), \ \ \ \ h(x) = \sin\!\left(3x\right).$$ If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer.

$\left( 0 \right) +$ $\left( \cos\!\left(3x\right) \right) +$ $\left( \sin\!\left(3x\right) \right) = 0.$