There are an infinite number of solutions to this as you can probably infer from the graph below:
However, if you mean within the range 0 to 360° then use the calculator in the form x = asec(2.5) to find the first one:
$${\mathtt{x}} = {asec}{\left({\mathtt{2.5}}\right)} \Rightarrow {\mathtt{x}} = {\mathtt{66.421\: \!821\: \!521\: \!798^{\circ}}}$$
If you look carefully at the graph above you will see that the next one is obtained by subtracting this from 360°
There are an infinite number of solutions to this as you can probably infer from the graph below:
However, if you mean within the range 0 to 360° then use the calculator in the form x = asec(2.5) to find the first one:
$${\mathtt{x}} = {asec}{\left({\mathtt{2.5}}\right)} \Rightarrow {\mathtt{x}} = {\mathtt{66.421\: \!821\: \!521\: \!798^{\circ}}}$$
If you look carefully at the graph above you will see that the next one is obtained by subtracting this from 360°