2cos(2theta - 20degrees) = 1

Sure, let's solve the equation step by step.

1. First, we need to isolate the cosine function. We do this by dividing both sides of the equation by 2:

   cos(2theta - 20degrees) = 1/2

2. Next, we need to solve for the angle. The cosine of what angle gives us 1/2? We know that cos(60 degrees) = 1/2. So:

   2theta - 20degrees = 60degrees

3. Now, we solve for theta by adding 20 degrees to both sides and then dividing by 2:

   2theta = 80degrees theta = 40degrees

So, the solution to the equation 2cos(2theta - 20degrees) = 1 is theta = 40 degrees.