You can see that all three points are 1 unit away from the origin, and that points B and C are always opposite each other with respect to the origin. So you can consider line BC as the base of the triangle with length 2. To make the area of the traingle a maximum you want the line OA to be at right angles to line BC (if you'd like a beter explanation as to why this is so post back). Consequently to maximimize the triangle area you want angle 3-t to be at right angles to angle t, or in other words either:

3-t = t + pi/2

or

3-t = t-pi/2.

Solve for t.