How do I find the exact value of this expression

sin (π/6) + tan^2 (π/3)

I know the answer, (7)/(2), but I want to learn how to get to that answer. Could someone show me the steps please? Also, please don't use a calculator, I want to know how to do this by hand. Any help is greatly appreciated. :)

These angles appear in the 1, √3, 2 right angled triangle where sin (π/6) = 1/2 and tan(π/3) = √3 so,
sin (π/6) + tan^2 (π/3)
= ½ + (√3)²
= ½ + 3
= 3½
= 7/2

There are two reference triangles you ABSOLUTELY HAVE to memorize

the 45 - 45 rt triangle also know as the π/4 reference angle

the 30 - 60 rt triangle also know as the π/6 - π/ 3 reference angle

sin (π/6) = 1/2 WHY? because the π/6 angle is 30º and I have memorized the sin of that angle

tan (π/3) = (√3/2) / (1/2) = √3 WHY? because the π/3 angle is a 60º reference angle and I have memorized the values for sin and cos and generate tan when it is called for

sin (π/6) + tan^2 (π/3) = 1/2 + (√3)^2 = 1/2 + 3 = 3 1/2

See note also:

sin(pi/6)=1/2
tan^2(pi/3)
=[tan(pi/3)]^2
=(sqrt3)^2
=3
So,
sin(pi/6) + tan^2(pi/3)
=1/2+3
=7/2
Note:
pi/6=180/6=30
and sin30=1/2
pi/3=180/3=60
and tan60=sqrt3
Hope that helps