For f left parenthesis x right parenthesis equals sine x​, negative StartFraction pi Over 2 EndFraction less than or equals x less than or equals StartFraction pi Over 2 EndFraction ​, g left parenthesis x right parenthesis equals cosine x​, 0less than or equalsxless than or equalspi​, and h left parenthesis x right parenthesis equals tangent x​, negative StartFraction pi Over 2 EndFraction less than x less than StartFraction pi Over 2 EndFraction ​, find the exact value of the composite function. f left parenthesis g Superscript negative 1 Baseline left parenthesis StartFraction 15 Over 17 EndFraction right parenthesis right parenthesis