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The exact value of sec 4pi divided by 3 is 1/3.
cos(195) = -0.965925826289
cos20 x cos40 x cos80 = 0.0300 radians = 0.125 degrees (the value for radians is given to four decimal places, the value in degrees is exact)
In a trigonometric equation, you can work to find a solution set which satisfy the given equation, so that you can move terms from one side to another in order to achieve it (or as we say we operate the same things to both sides). But in a trigonometric identity, you only can manipulate separately each side, until you can get or not the same thing to both sides, that is to conclude if the given identity is true or false.
tan u/2 = sin u/1+cos u