The trajectory $(t)($angle as a function of time$)$ of the harmonic pendulum can be expressed as

$(t)=$Acos$(t+)$

$A=\sqrt[\phantom{2}]{{}_0^2+(\frac{{}_0}{}{)}^2}$

$=-arctan(\frac{\frac{{}_0}{}}{{}_0})$

It depends on the frequency $$ and the initial conditions ${}_0=(0)($initial angle$)$ and ${}_0=(0)={}^{}(0)($initial angular velocity$).$

Write a Python function theta $()$ to compute the trajectory for given time points. The function must do the following:

takes an array $t$ of times as mandatory argument;

takes the mandatory argument omega to set the frequency;

returns an array of the same size as $t$ in which $(t)$ was evaluated for each element in $t$;

contains a doc string that briefly explains the function and the arguments that it takes;

takes an optional argument the ta $0$ with default value $\frac{}{6}$;

takes an optional argument omega $0$ with default value $0.$