find the exact value of each expression without using a calculator

sin pi/5 + tan^2 pi/3

= sin pi/5 + (tan pi/3)^2

As Pi/3 = 180/3 = 60 degree and pi/5 = 180/5 = 36 degree then

= sin(36) + (tan(60 degree))^2

= sin(30 + 6) + (√3)^2

= sin30cos6 + cos30sin6 + 3

= 1/2(0.9945) + √3/2 (0.1045) + 3

= [(0.9945) + (0.1045)√3 + 6]

= [(0.9945) + (0.1045)(1.7321) + 6]

= 7.17550445

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