Evaluate sec((2pi)/3)^2

$\sec^{2} (\frac{2 π}{3})$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because secant is negative in the second quadrant.

${(- \sec (\frac{π}{3}))}^{2}$

The exact value of $\sec (\frac{π}{3})$ is $2$ .

${(- 1 \cdot 2)}^{2}$

Multiply $- 1$ by $2$ .

${(- 2)}^{2}$

Raise $- 2$ to the power of $2$ .

$4$

Evaluate sec((2pi)/3)^2

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